By basing a fixed reward on a proof of work Bitcoin prevents a Sybil attack. You have to think about how your protocol will overcome a Sybil attack in order to make it work. I don't see a decentralized way to know exactly how much hash power someone is providing.
You need a centralized entity to determine and enforce rules about splitting hash power.
You need a centralized entity to determine and enforce rules about splitting hash power.
The "Rules" of bitcoin are determined and enforced via code. With proper code-modification, these new "rules" would be implemented in every computer mining or running wallet software, therefore making it decentralized. Correct?
*EDIT: Plus, those rules could be variable just as difficulty is. Instead of a target block time, you have a target reward (per "user")? Maybe?*
maybe this can be sensibly revised and applied to bitcoin itself in some way but still maintain bitcoin as its name... just like switching POW to POS or POS to POW 
