they can already do that with the fee, 10ks to everyone that is running a node, per day, at least they have a free transaction
Is there a block reward scheme for full nodes? I am interested in joining one. I have a full node.
no there are not reward of any kind, sadly, otherwise i would run one
The big mining pools could offer a small payment as an incentive to people running nodes. It could help pay the small costs of running a node like wear and tear on hardware, and power. The biggest pools must make a handsome profit, they could afford to give a small part of it for running nodes, but they probably won't.