Nope won't happen cause if the miners accept the abolition of the cap then it's a free for all with unlimited coins and they become inflationary exactly like the fiat system which is the polar opposite of the ideals behind bitcoin.
It would depend on what the new cap would be set to. If the TX fees are not enough to cover miners electric costs then the cap could certainly be increased to continue to give miners incentive to mine while giving bitcoin more time to grow