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?
I don't think it's the best bit of bitcoin to be mined. The number of bitcoins in the market is limited, and the number of passepartout in the market is also some, and it is not affected by the total mining of bitcoins.