If you "remove fees", and I contact a mining pool and offer to send them a payment to confirm my transaction in their next block, how are you going to prevent me from doing that?
I like that method better. Basically you would have to be lucky enough to pay the right pool. It is a lottery whether the person you paid actually wins the block or not. This would effectively set fees to zero for normal transactions and if someone really needs something expedited then they can try their luck on guessing who the next person to win the block will be.