You didn't ask me, but I can't help but chime in on this one. The two cannot be easily decoupled. It's like Siamese twins. Each is dependent on the other. The blockchain works because the participants are rewarded. Without a reward, there will be no blocks.
Well, I guess I could see some scenarios where blocks would be produced for different reasons. The NSA would be a likely "altrustic producer" in some weird privacy coin, for sure. Facebook too. Perhaps Alexa could yield block producer rewards based on a measure of your "usefulness" to AMZN?