The intention of the original bitcoin design was that the miners would transition from minting new coins to earning their money from transaction fees. Bitcoin was also envisioned as an actual currency, routinely used to pay for things though.
It's unlikely all the miners would agree, so bitcoin would fork (again). One fork would dispense with the cap and I think that would probably crash its value.
Since the number of transactions is likely to go down with increased transaction fees, the number of miners in the other, capped fork would probably decrease, and the hash difficulty would decrease, until transaction number, price, and miner expenditure reach a supply vs. demand equilibrium. That would seriously compromise the security of that fork, which would probably also crash its value.