You could just remove the reward, any one can mine new block out of the mem pool, if two blocks or tx are in common, a determinstic algorithm could be used to select between the two.
I agree with you. The error in most crypto is the reward, which gives rise to strategies that do not necessarily induce the desired properties. I also think that the only viable kind of crypto currency is where the validation/consensus decision is taken on a voluntary basis, the "reward" being that the system in which you are invested, keeps running correctly.
However, you still need a kind of deterministic decision *that is hard to game* (because you can do "proof of work" like calculations to get the deterministic solution in your advantage). This is why a kind of PoS signature scheme is necessary in my opinion.
With the hash of previous block in the header including timestamp for me it's enough to prevent sybil attack. Checkpoint could be made every 100 blocks and hashed in the chain.
Checkpoints are no solution, because they are just another consensus problem. If you have two conflicting check points, which one is the "right" one ? You've just transposed the block consensus to the check point consensus.
Yes, you can *individually* decide that you won't allow any old modification of consensus. But there is no guarantee that the rest of the network will follow you.
But mainly, yes, PoW is a bad idea, and rewarding (with fees or coin creation) consensus deciders/maintainers is also a bad idea.