Hannibal choose to go trough the Alps to achieve tactical and strategic iniciative over a powerfull enemy.
Alexander just throw a tantrum.

Who'd Alexander have left to fight by that point?

Steak said:

Who'd Alexander have left to fight by that point?

His own ego.

Rathurue said:

His own ego.

Right. Don't need an army to deal with that.

Meanwhile, with Rome, even if you don't hate them and they didn't pose an existential threat to you and your country, taking them on would be way cooler than marching across a desert into the unknown.

My lord, that's quite the mane on Alexander

Steak said:

Who'd Alexander have left to fight by that point?

Their were still plenty of kingdom/sate in the Indian peninsula, but It's would have been near impossible to conquer them all with the limited ressource of Alexander at this point.

Ironacly, a large portion of the peninsula would be fall under control of the Maurya Empire, not long after Alexander death.

He could also go north and try to conquer China, that at the time was just a loose confederancy that still fight with chariot, bronze age style, but the journey may have been more painfull then going to india.