...
If there is a better way to organize a neutral global money system, we should have it penned here and get a nobel prize in economics.
FYI there is a better way, it's called Proof of Stake mining, it's working for a variety of altcoins, they have all avoided the inevitable downfall of PoW systems (expensive + low security).
From what I can see, Proof of Stake system doesn't really solve the problem that Bitcoin is solving. It puts a group of people at the center of its security model. In that sense the network is "owned" by the wealthiest of its stakeholders, which turns it into a form of private money, and we already have plenty of that.
Bitcoin, on the other hand, has a neutral algorithm as an ultimate judge for people's performance. That's how it ensures that any attack on it is not permanent and can be overturned with the same 51% mechanism. All Proof of Stake systems in that sense are already 51% attacked by default, and their position is static over time.
If so it's a HORRIBLE idea because it creates unnecessary cost barriers to getting into Bitcoin mining.
Correct. Mining-less systems regardless of their initial distribution of money have an asymptote that leads towards centralization essentially turning any such system into a private enterprise.