I was wondering if pools actually interested to share some of the fees they get with individuals running full nodes relaying and supporting their pool?
Or doing that brings any benefit for them at all?
You will find that some pools will already have their network configured to optimally distribute blocks as fast as possible all around the world.
Well I do at least
Being a full node does not really mean much unless your node is able to get blocks to other pools faster than a pool can already do that itself.
However, core bitcoin itself is not very fast at relaying blocks.
I guess you could say: your competition is this:
https://bitcointalk.org/index.php?topic=766190.0