I think by the time a PoS system become big, it will be too expansive to buy it, even for the wealthiest. Therefore they will need to buy it somewhere in its ascent, and that will deter the market to use it and another PoS system will win the adoption race.

And all of that is assuming there will be only one dominant currency. Which will probably not be the case. A lot of the socialist thinking come from the false premise that free market lead to monopolies. In the same manner that there is not one corporation which address each human wish, there will be no unique money. And if the wealthiest will not be able to even capture one succesful PoS system, a fortiori they won't be able to capture all the succesful PoS system.

I need to do some research to see what incentives are planned fo "miners". I would be surprised if there were not.
It was not a rush for money, it was a rush for a highly speculative investment.

There is no money here and now in the cryptos landscape, only speculative investments. In your reasoning you can't treat something that is only a speculative investment as if it was already the money system of the society. It's a logical fallacy.
A lot of Austrian economists have no clue either. How many of them disdain Bitcoin because it doesn't fit Mises' regression theorem?

See Hayek for the competition in money. He did understand Austrian economics and his views on money are more relevant than the all of the Austrian crowd together imo.
XCP is the antithesis of a scam. It was distributed by proof of burn, even the developpers had to burn their BTC to get some. It's arguably the fairest coin distribution since Bitcoin.
They are doing both. They will issue X ether via an IPO and then 0.4*X ether will be distributed each year via PoW.