It's the combination of basic plot structure and Disney's family friendly message.
Plot structure and good storytelling
- A problem arises, no one can fix the problem, the hero currently cannot fix the problem, but can work towards solving it. In the end, the problem is fixed.
- The viewer is generally supposed to identify with the protagonist, as both are often exploring an unfamiliar setting.
- Most protagonists carry emotional scars, their personality is driven by their response to a tragedy in their life.
- Stories should try to limit the amount of characters that are present, to avoid creating confusion for the viewer.
- Your parents always help you.
- You (the child) are the hero.
Available parents would solve all the problems.
Combining the two, you should see where the issue lies: if the child has its parents nearby, then the parents will be able to solve the plot for them.
In the interest of plot development, that can't happen. The parents must either be unavailable, or unable to assist in the plot in any way.
Note that when we see living parents, they are almost always hilariously unskilled at what they do.
- Yasmine's father is wholly incapable of ruling. Although he means well, he is childish, easily swayed, and doesn't even correctly identify Yasmine's desires.
- Aladdin's father, though he cares for Aladdin, lets his greed and materialism get in the way of his familial ties, thus rendering him unavailable (and a situational obstacle to Aladdin, e.g. by smuggling the hand of Midas with him).
- Mufasa is a strong and just ruler. He expertly rules the Savannah (compare him to the sultan...). He would be able to overthrow Scar without anyone fearing that Mufasa might fail. That would make for a boring story, so Mufasa dies and becomes unavailable (with the exception of cloud-Mufasa's inspirational words, which may have been a hallucination by Simba).
- Sarabi (Simba's mom) has never been in the picture, even if alive and present. We could call the Lion King sexist for clearly putting men above women. While Nala has a stronger personality, her role is pretty much reduced to asking Simba for help, and that's about it. Arguably, Shenzi the hyena is the only saving grace here, as she is the leader of her pack of three.
- Finding Nemo is a bit special here. Although many see Nemo as the protagonist, I would argue that Marlin is the protagonist here. He's the one making the journey, facing the dangers and living in insecurity. Nemo, comparatively speaking, went on a field trip to Sydney. When you look at the moral message of the story, it focuses on how overbearing parents mean well, but should learn to relax more.
- Maurice, Belle's father, is clearly incapable of leading his family. Belle consistently takes care of him: she hands him tools that he can't find, she does the outside chores because he father is deemed mad by the townsfolk, she sacrifices her freedom for Maurice's. And when Belle is not around, her father can't even convince the townspeople of anything, they immediately twist his statements into proof that Maurice has gone mad. Without Belle, he likely would'nt have escaped the mad house.
- Cinderella's story is driven by being abused by her family. To avoid nasty inferences about how your family can be horrible to you, most children's stories will always make the step family horrible, not the biological family (e.g. the queen in Snow White is her stepmother, as is the stepmother in Hansel & Gretel who wants to get rid of the children while their actual father loves them). So if Cinderella needs to face familial abuse, she needs to be in a step family, which inherently means that she has no real family anymore.
- Lilo and Stitch is a "buddy movie". Part of what drives Lilo is the lack of affection she gets from not having parents. He sister takes care of her, but is too busy with her own life to give Lilo the continual love and affection she needs. Stitch is very specifically a substitute for Lilo's lack of parental affection. By getting to know Stitch, she matures from a child (connected to its parents) to an emotional adult (connected to their friends).
- The parents in Frozen were the only thing that kept Elsa's powers in check. As the plot is mainly driven by Elsa's emotional outrage at how people respond to her powers, she can't have her parents around to give her emotional support and talk her down (it precludes the plot).
Footnote: Notice how a lot of one-parent families end up with a parent of the opposite gender. There is a common trope where a mother innately understands her daughters, and a father innately understands his sons. By using different genders, the likelihood of misunderstanding increases (e.g. how the sultan doesn't understand Yasmin's desires) and therefore makes the parent more unavailable to assist the protagonist child with their issues.
Disney cannot do the opposite.
The previous chapter is clear: parents solve all the problems and would preclude a good plot in a family friendly movie.
It's interesting to note that Disney is wholly incapable of moving away from this, without infringing on their family friendly message. Let's look at the alternative, where the parents are present and capable, but cannot solve the plot.
Why can't they solve the plot? If they're capable of doing so, and they are present in the child's life, then the only remaining option is that they either don't care about the problem, or they ARE the problem.
If they don't care about the problem, that means that the child protagonist must go against their parents in order to resolve the plot. While this may arguably work equally well when you consider children the target audience of the movie, I doubt that many parents will want to take their children to go see a movie that teaches the child to disobey its parents.
Note that there are a few movies where children do go against their parents, but they are usually focused on teens instead of younger children, and the parents are explicitly shown to be caring but misguided (e.g. How To Train Your Dragon).
If they are the obstacle, the implication becomes even worse, basically teaching the child that your parent is the problem. Notice how there are no Disney movies where a child has to fight their parents, for this exact reason. It creates an interesting plot, but the moral lesson diverges from what Disney wants to tell.
One of the examples you listed fits this to a tee: Jungle Book. Mowgli is an orphan, because he ends up lost in the wilds. If Mowgli were to have parents, what would that say about them? That they lose their child, and that the child actually likes living without his parents.
Notice how Bagheera needs to explain to Mowgli that he belongs in the human world. In the end, Mowgli still doesn't agree but he does respect Bagheera's advice. Imagine the implications if Mowgli didn't want to go back to the human town where his parents live.
Interestingly, there is one exception to this rule: Inside Out. Both parents are alive and well, and it is highly implied that they are (part of) the cause of the problem. Riley does in fact rebel against her parents, but the plot also makes sure to explain that Riley is a slave to her emotions, thus making her the victim, not the perpetrator. Also, the parents eventually admit that they are part of the problem and take responsibility, which avoids an undesirable plot resolution.
Condensing background characters
This is also an important one. Notice that all parents we have seen are background characters, because the focus is on the protagonist child who is dealing with the plot.
Background characters should exist (to make the story layered), but the number of background characters should be limited. A great example of this is The Lion King 1.5 : Hakuna Matata.
In the movie, we actually meet Timon's family: his mom and uncle Max. However, Timon was also slated to have a father. Here he is, on the right. Based on his character design, you can tell a lot about his intended personality. His hair resembles that of uncle Max, but he has a friendlier face. However, he looks less emotional than Timon's mom. It seems likely that Timon's dad would basically have been "meerkat Mufasa": pragmatic, not driven by emotion like Timon's mom, not negative about Timon like uncle Max is. Looking at Timon's mom's scenes, it makes sense that the "goodbye" scene would have been Timon's dad, because it was out of character for his generally overbearing mother to suddenly agree with Timon leaving the nest. It makes more sense for his fathr to agree, and take the responsibility of consoling the mother on himself.
However, there was a problem here. Timon's family only gets limited screentime, and a handful of lines. If Timon's father is part of the movie, that means that this limited screen time would be shared by three background characters.
There simply wasn't enough screen time to create exposition for three background characters. In the end, they merged Timon's mom and dad into Timon's mom (she took all of the Dad's lines). Notice how they opted for the parent of the opposite gender, as per my earlier footnote.
This is especially true for a movie directed at children. The story is kept simple (not many plot twists or ambiguous scenes that get revealed to "only be a dream"), with a limited amount of distinct characters.
There are examples of this in your list:
- The parents in Toy Story are wholly irrelevant. Even Andy himself is a background character. If they weren't moving house, neither parent would've been relevant enough to be part of the plot. But the moving situation required a parent to drive the car.
- Ariel doesn't need a mother. Again, there is a point to be made that Poseidon is of the opposite gender (thus explaining why Ariel's desires are not addressed by her father); which gets further complicated with Poseidon being a god (therefore omnipotent, thus making the mother unnecessary in terms of providing for Ariel). The main focus of the movie happens outside of Poseidon's view, which renders Ariel's parents as background characters, likely to be condensed into a single character.
- Bambi mostly focuses on how a naive deer makes its way through the world alone. It makes sense to cut down on the amount of family that such a character has. Similarly, Dumbo's adventures are driven by no longer having his mom around.
Parents can be dead/missing/irrelevant for many different reasons:
- Their presence precludes the plot.
- Their presence, combined with the plot, ends up impling bad things about family values. Disney puts family values first, and therefore has to sacrifice the parents' presence in favor of the moral message.
- If they are sufficiently irrelevant to the plot, parents can be condensed into a single parent for the sake of lowering the amount of characters that we need to know about.