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.
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?*