He wished to be a prince, his royal entourage hypothetically included several people capable of assassinating Jafar on the order, it was just down to Aladdin being a stickler for being an active participant in proceedings that hindered him taking that less direct route.
You don't even need to watch the sequel to see that, as genies being bound by specific rules is the whole point of tricking him into becoming a genie.
Though after Aladdin wishes for the Genie's freedom, it really opens a can of worms as to what that means. Sure, I guess he's free to roam the earth, and no longer bound to grant wishes. But at the same time, has he now lost that power?
Because Disney ending aside, you would think an unbound genie with his full powers would be something that only ends badly.
A Djinn's wishes are meant to serve as a lesson about understanding what you actually want while Shenron's limitations are more about keeping any mortal who can summon him from stepping beyond their bounds, especially since we now have the super dragonballs implying significant limitations on what regular dragonballs are capable of in comparison.
Honestly it'd be interesting to see a comparison of wish granting powers to understand what their limitations imply about their roll in the story.
In Dragon Ball Z, collecting all 7 dragon balls allows you to summon an all powerful dragon that will grant you one wish, for anything you desire. Wishing for someone's death or resurrection are not limitations