If there would be only 1 miner, happily mining on his CPU, blocks could handle exactly the same amount of transactions. We don't need more miners to process transactions, that doesn't change how many transactions Bitcoin can handle at all
As to me, this is an absurd situation
Generally, to claim that higher fees lead to more competition between miners, you have to solve the following dilemma, i.e. to explain how it is possible that users are competing between themselves for the inclusion of their transactions in the new block by increasing the amount of money they are willing to pay for that, and at the same time (as you claim), the competition between miners rises as well. I guess you can't have it both ways at the same time in a free market
But maybe this isn't a free market because the blocksize has been artificially retarded by the Core Politburo? That could certainly cause fees and miner competition to go up simultaneously... Hmmm.