But why did they omit Euron's disfiguration?
The first answer I'd offer is simply that it is omitted by irrelevance. I haven't read the books, but if Euron's disfigurement doesn't change the plot in any way, it's not required.
This can be for budget reasons (or not overly complicating the story), but I can't find any proof to support that.
Secondly, you have to consider that you have to look at the characters in a TV show, but not in a book. Describing Euron's disfigurements in a book would take up a page and never really effect the rest of the story.
However, seeing a disfigured Euron would be a permanent thing that permeates through all of his screen time.
Similarly, Tyrion's disfigurements from the battle of Blackwater, while present, are a whole lot easier on the eyes in the TV show. In the book, iirc, he lost his nose and looked really horrible. Again, you can't do that to a main character.
This is different from the books. In the books, all scenes can continue as planned, and we still read what Tyrion has to say and evaluate him based on his character, without having the image tainted by looking at a disfigured face.
In the same vein, imagine if a character has an annoying high pitched voice. You could still give them a long monologue in the book (and mention that the listeners are annoyed by his voice) without having the reader be annoyed by the annoying voice_.
You couldn't let that same character do it in a TV show, because you would force your viewers to sit through a monologue that's maybe very important to the plot but horrible to have to listen to.
Lastly, from what I've heard of the Euron storyline, there is supposed to be a possible interpretation of Euron being likable. He has charisma, he can get people to see things his way (e.g. in the TV show, how he made himself king instead of Asha/Yara).
The Hound was often interpreted as a "bad guy" in the first seasons. This wasn't because of his actions (one of the first things we see of his character is rescuing a jouster from the Mountain who "cheats" and tries to kill him after the joust; and also killing the people who try to rape Sansa), but he is still disliked because of his general demeanor. His facial disfigurement makes the viewers interpret him as a (potentially) a bad guy. It takes a lot of character development to change the viewer's opinion, and even now there are still people who consider the Hound more evil than good.
If the next season will want the viewer to question whether they like Euron or not, then it might be better to omit the facial disfigurement. That way, the viewers aren't being suggested that he is a bad guy, and it is much more open to interpretation.