That design decision comes from a fundamental (but rarely discussed) design requirement Satoshi had, which is that all entities in Bitcoin must be able to join and leave at will, unannounced and anonymously.
If you want a purely decentralised system, this is a "hard" requirement, it's non-negotiable. Bitcoin simply wouldn't work without it.
If you are willing to relax the decentralisation requirements a bit so that there's some kind of explicit join/leave protocol and participants have some verified identity, or you can rely on non-standard hardware, then you don't need PoW anymore. You can just use chains of digital signatures, for example. Or you could use PoW as a means to do a randomised leader election like Bitcoin does, but where each miner just uses a single CPU because the amount of hashing doesn't matter (fraud can be punished via the legal system instead).
Nice start, you seem to have solved even the problem of easy anon entry/exit.