no
the block reward is the miners payment. and miners can accept or reject any transaction they like.
This is stirring smoke, miners tend to unite in pools, they get block rewards and fees are expected to slowly get a little bigger. And they could reject transaction, but no one does it without a really serious reason (or just noone does it), because they lose money. Ability of miners to reject transactionns has nothing to do with their incentive to enable transactions to earn money. You are totally moving the target.
Look I'm dropping out, let the readers decide who is right.