Why do we need transaction relayers? What vital function do they provide?

Miners need to be connected to each other, and to transaction creators (individual users, exchanges, merchants, online wallets, etc).

And transaction creators need to be able to connect to miners, but it seems to me transaction fees should certainly be enough incentive for miners to arrange for there to be plenty of opportunity for transaction creators to send them fee-paying transactions (it's cheap to run nodes that have tens of thousands of incoming connection slots).