Most likely such protocol will turn into a cat and mouse game.
What exactly do you mean by that? It exists already. It rewards relays for contributing bandwidth to the network. Theta token uses it but it's rigged so that the node reward is just peanuts. They have this separate toke for rewards which is much weaker in value than their primary token which is for staking. This could be done is a way much profitable way for the contributor where the network has just one more scarce token for both staking and rewards.