Solution to PoW vs PoS, etc

So we have the issue of PoW vs PoS in the altcoin world now. Both, including Zec’s, have the same problem: people with more money and resources have the ability to mine or stake more and ultimately can control the market. Rather than switch to PoS, etc to keep things even, we need a better way:

Solution: PoP - proof of power. Share value based on hash power to generate block. Every miner (address) can only mine X blocks per round. Transferring between addresses costs more than makes it profitable to use multiple addresses. Using existing difficulty algorithms, simply monitor the hashrate / shares over time into the network by a miner / address. As the miner adds more power, increase their difficulty so they can only mine X blocks. In this way, all that is accomplished by having more mining power is the ability to mine more difficult blocks for the same reward. This ensures everyone, regardless of power or stake, can earn an equal amount over any time regardless of compute power.

It seems like this is the most logical solution to the whole CPU vs RAM vs some other resource constrained PoW. Don’t try to constrain it, just only reward X over time regardless of how much power is used. This would make poor and rich equally capable of earning coins in any given time and would theoretically not be “hackable” if PoP was based on consensus like other algorithms.

Thoughts on why this type of PoW/PoS would or wouldn’t work? Why it is or isn’t better than current PoS and PoW concepts? Obviously, a full blown algorithm would still need to be thought through.

Addition: keeping track of current address difficulty is as simple as storing it in the last block mined by that address. So everyone would start out with the first block being 0 difficulty - super easy - but would always mine at their last known difficulty on future blocks.Even if they stop mining and lower their power, the system still gives them last known difficulty until they mine a block at loser difficulty. So no way to jump in and out to lower their difficulty.