This would require that nodes prove they are in fact running a node (which is surprisingly difficult, especially when payments would instinctive people to fake running a node). This would also mean that Bitcoin would no longer mine via PoW (at least not exclusively) but rather would be mined via PoN (proof of node) or a combination of PoN/PoW. It is said that if Bitcoin were to be forked so that it no longer uses PoW (among other things) then it would no longer be considered Bitcoin