What are you talking about? With Proof of Work and Proof of Stake, everyone is ALWAYS rewarded for their shares. What you're proposing is that a chunk of miners randomly be rewarded the entire block, regardless of how much they are contributing to the network. This creates the chances for someone to NEVER get rewarded.
Did you even put any thought into your idea or you just simply came up with it while daydreaming and decided to post it to increase your post count?
You claim that PoW is not sustainable yet your idea is very similar to it. Why would you even think that they are not sustainable?