I think that was the Genie’s curse.
I remember escaping the cave was the first wish. The second was becoming a prince. The final wish was releasing the genie from the bottle. Am I missing one?

The supposed wish to save Aladdin from drowning was #2.

Genie getting them out of the cave, I believe, was to prove to Aladdin he could do it. It didn’t count as a wish.

Wish 1: Become a prince.
Wish 2: Saved from drowning.
Wish 3: Free the genie.

I’m confused at what the question is. He was bound to an eternity of serving others, which is why Aladdin freed him. He was limited to three wishes because – well, just because. It’s always three wishes in movies.

Because,

Three is a magic number.
Yes it is, it’s a magic number.
Somewhere in the ancient, mystic trinity
You get three as a magic number.
The past and the present and the future,
Faith and hope and charity,
The heart and the brain and the body
Give you three.
That’s a magic number.

It takes three legs to make a tri-pod or to make a table stand.
It takes three wheels to make a ve-hicle called a tricycle.
Every triangle has three corners,
Every triangle has three sides,
No more, no less.
You don’t have to guess.
When it’s three you can see it’s a magic number.

A man and a woman had a little baby.
Yes, they did.
They had three in the family.
That’s a magic number.

Odd. Reading the source story (Ala-el-din and the Wonderful Lamp, from the Tale of One Thousand Nights and One Night), there were TWO Jinnis. The Slave of the Ring, who got him out of the cave, and the Slave of the Lamp.

from the Slave of the Lamp:

he’s wished for food twice,
wished for the Wezier’s son to be stuck in a closet on his wedding night to the sultan’s daughter,
wished for a handsome dowry for the Sultan’s daughter,
wished for a “bath like the world has never known”,
wished for 12 damsels dressed like king’s ladies,
wished for a palace
wished for a carpet – not a flying carpet. Just a carpet.
wished for 10,000 dinars
wished for an addition to the palace

Then the lamp is stolen from him, and he’s back to the Ring
Wished to be taken to his stolen palace
Wished for the palace to be taken to China

So…

My guess is that the real story would have been long and boring, and they had to cut it short somehow, and keep it from being the tale of Aladdin and his Magic Butler.

Freebe on a technicality #1 get out of the cave
real wish #1 become a prince
real wish #2 saved from drowning
real wish #3 free the genie.

Any more would be just plain greedy, wouldn’t want to rub the genie the wrong way.

I like @Blondesjon‘s Trinity answer.

3 wishes makes them precious. Beginning, middle and end…we can wrap our MINDS around 3 wishes all at once. Who wants to read a story about 1,000 wishes, were Aladdin ends up craving a toasted marshmallow?

You think a powerful genie would want to hang around forever listening to some greedy prick’s personal with list? Actually, one wish is plenty, anyway. Just wish for unlimited wishes. Knowing this, genies have little patience with people who can’t figure this out given three guesses.

“RULE ONE! I can’t kill anyone. So don’t ask. RULE TWO! I can’t make anyone fall in love with anyone else. RULE NUMBER THREE! I can’t bring anyone back from the dead. It’s not a pretty picture, I DON’T LIKE DOING IT! Other than that, you’ve got it.”

“Three wishes to be exact. And IX-NAY on the wishing for more wishes. That’s all. Three. Uno, dos, tres. No substitutions, exclusions or refunds”

I had awful parents…

Now I want to watch Aladdin.

@livelaughlove21 , @Seek_Kolinahr , This is an perfect example of the “disneyfication” of the classics to create not only a new story, but also a costume character for the parks.

I think another interesting take on the magic lamp story is relate in the series Once Upon a Time in Wonderland.

I always wondered why Wish #1 couldn’t have been: I wish for 2000 additional wishes.