Proof of Work is the only true Consensus Mechanism for any truely Decentralized & Trustless Cryptocurrency. It currently has no better/proper replacement that I'm aware of.  And it simply means to Prove Miners Works before they are rewarded and their works accepted.
Higher price tend to attracts more workers/miners (possibly with more powerful miners to be able to keep up with mining difficulty) thus making the Network more secure against 51% attacks and increasing the energy usage.


By the way, Bitcoin is a Freedom System that isn't supposed to limit users like PoS does with stake limit, lock limit, consensus limit etc . It's dangerous to limit the freedom its features gurantee to people while trying escape or survive a tyrannical opposite system . The proper way to solve problems on the Network is to creatively build on the existing foundation/principles like on the Permissionless feature you mentioned. If you are worried about 51attack or the so called fake node, then create a decentralized identity system which anyone can easily have, then get anyone who wishes to be monitored less (or have a smooth stay on the network) probably against 51% attack to verify their identity. Miners identity information must be hidden/private and should only controlled by them. Once there is an attack from a miner or group of miners the Network can have their identities unmasked via consensus. You can also use ID scheme to build miners reputation... If you choose only reputation without ID , I think that could easily be cheated.