Right now we're approaching about 17 million out of 21 million possible bitcoins. When we reach the max supply, what incentive would miners have to continue mining and verifying transactions? Sure they can still collect fees, but why not mine newer and more profitable coins where they have the chance to collect both fees and new coins?
What's stopping the entire blockchain from grinding to a halt, prohibiting users from conducting transactions, and thereby making bitcoin worthless?
That was the whole point of establishing a fee market. Recently, there was at least one block mined where fees were greater than the block subsidy. It's likely that the fee portion of block reward will be greater than the subsidy
long before the supply is mined out. Hopefully that transition is smooth, but the jury is still out. This is all still a big experiment.
The altcoin question doesn't seem important; it already applies now. Why not just mine more profitable coins? Probably because Bitcoin is much more stable and reliable as a long term investment. Altcoin markets are also much less liquid, so big players who want to invest lots of capital into mining are limited in their choices.