As a matter of fact, investigating pooling pressure and mining centralization threats in bitcoin I've become convinced that an affirmative approach to the above question is inevitable in the framework of any solid solution to the core problem of mining centralization.
I don't see how paying full nodes some sort of reward for running could have any effects on mining and mining pools. That just adds an additional reason to centralized another aspect of bitcoin (running a full node) and if we assume there were any centralization in mining the same entities would also run full nodes and take the control in that area also.
I didn't suggest that, paying rewards to full-nodes. I'm just reminding the fact that the main incentive behind running a full node was designed to be a strict requirement for participating in mining which is absolutely omitted with the current situation in the scene. If instead of tens of pools we had thousands of miners actively generating their own blocks, i.e. in a truly decentralized mining scene the actual value of running a full node would have been discovered already. Decentralization of mining is the key to this problem.
Many businesses need full node, not only miners. Payment providers, exchanges, etc. And it's not so expensive to have one.