The chronology in universe (and out) is
- Aladdin (1992)
- The Return of Jafar (1994)
- Aladdin (Cartoon)
- Aladdin and the King Thieves (1996)
In the 1992 Movie Aladdin free's the genie,
so he is no longer his master in the time of the cartoon.
Just his friend.
Genies do only have the ability to grant their master 3 wishes.
As a narrative point, outside of wishes,
the vast majority of genies' magic seems only to result in transient changes to the world.
This also seems true in the films, where the genies are constantly doing various magics, most of which are gone by the next scene.
From a narrative perspective this makes sense, other wise the genie could literally solve every problem.
From Return of Jafar 1994:
It seems like some people (Abis Mal) suspect that any magical change the genie makes on the world (in this case summoning riches) will not last, unless it is backed up by a wish:
Jafar: Indeed. You will now wish me free of this wretched lamp!
Abis Mal: No! My wish! You got what you wanted! Now it's my turn!
Jafar: But you don't need to waste your third wish. You want the sunken
treasure of Coeur du Mer? It's yours!
Abis Mal: (cheering and laughing
excitedly) Yes, yes, yes! Yes! I love it! I love it! Silver! Lots and
lots of it! Oh, I'm so excited! So this means I could have more stuff?
I always wanted one of those! Nice! More! More! (Genie's hand is
smashed with the golden eagle statue)
Sultan: Oh, dear!
Jafar: Now, if it's obscenely excessive enough, perhaps you'd care to grant my
Abis Mal: Huh? What? Oh, yeah, right. Wish you were free.
Sure thing, yeah. I wish for Jafar to be... Wait. How do I know that
these things won't disappear once I set you free?
There are a few references to the freed genie being weaker e.g.:
Also From Return of Jafar 1994:
Aladdin: So, Genie, how does it feel to be free?
Genie: Seriously? I
love it! (breaking his back) OK, maybe my powers aren't what they used
to be. Let's say they're semi-phenomenal, nearly cosmic, (shrinking
short) but don't sell me short. I may be free, but I still have some
magic in me.
at the point in time Aladin is no-longer the genie's master, he can't force him to, and without wishes the genie might not actually be able to.
But in any case, Aladin doesn't want the riches,
He turned them down, along with the position of Vizar at the end of Return of Jafar 1994:
Iago: And so the bird lived happily ever after, wallowing in luxury as Aladdin's palace pal. (in the Sultan’s cushion bandaged
with his left foot and arms plus his head)
Sultan: Now, my dear boy or should I say, my new vizier?
Iago: Oh, say it!
Aladdin: Sultan, I'm very honored, but...
Iago: But?! What but? "But" is such a strong word!
Aladdin: I can't be your vizier.
Iago: What?! (grabbing the Sultan’s shirt) Sultan, the boy's talking crazy talk! Don't listen! (yelling at Aladdin) What more do
Aladdin: The world.
Iago: Look, personally, I'm with you, kid but let's take it one step at a time. (his beak was shut in bandages)
Aladdin: I mean... I want to see the world. I can't just stay in the palace. (looking at the city of Agrabah in balcony view) There's
too much to do, too much to see.
So Aladdin would rather live free as a Street Rat, than be tied down with riches.
I mean the Sultan knows he is the hero of the nation, and he is romatically involved with the Princess, so he's never going to really actually be poor.
But he cares not for the trapping of wealth, that is part of his characterization.
Transcripts sourced from Transcripts Wikia