This will only work if people are getting paid when they are running a full node. Unfortunately unlike mining Bitcoin people who run a full node is only running at a cost without really earning anything, they do this voluntarily in order to keep the Bitcoin network up and running. So really this "incentivizing" system is really the one to go if we want to see thousands (not millions) of people starting their own full nodes. But we aren't the problem here since we need someone like a organization or a corporation who is willing to pay people to  run full nodes for Bitcoin, they need to be willing to spend millions of dollars on a monthly basis for these people and just by looking on our current situation I don't see any big corporation doing it not unless there operations are heavily relying on Bitcoin payments.