see Proof of Stake designs achieve as low as a 4 second block speed with 100% protection from double spends.
This is half-true or maybe even false. The system protects you from double-spending as long as the ones who own the most of the money supply sign their blocks honestly. The system cannot ensure those few won't double-sign for the given block. We've already explained that it's designed to centralize overtime anyways:
it's because those who want to secure the network need those who are securing the network. In PoW, anyone's free to setup their hardware and start securing, but in PoS, it's down to those entities' judgment if new people can enter.
The difference I was trying (and failed miserably at it) to point out is that unlike POS in order to get more votes you don't have to make the other guys rich by doing so nor do you have to force them to give you a share of it in a redistribution of wealth.
They will keep accumulating wealth (coins) while you're going to keep losing as you will never afford to put aside as much money as they do.