[...] to pay people to run full nodes? there are already thousands of them doing it for free.
It's indeed practically meaningless for the original Bitcoin network as it kept a reasonable block size. But making a full node incentive part of the economic protocol might help to find proper responses to the block size controversy. It might make it more obvious that too high block sizes make it too expensive to have a healthy level of full node decentralization.
Even if you find way to pay full node which are very difficult to abuse and without locking big amount of Bitcoin, it won't solve block size controversy.
Without changing total bitcoin supply, each node only get very small amount of Bitcoin (which already mentioned above) and it won't cover cost of running full node.
Yes, the fixed mining reward distorts the incentivization too much to properly investigate appropriate rewards for running a full node. But the same problem applies to transaction fees. It is crucial to solve both issues before the mining reward approaches zero.