No, in PoW those with the most hashrate determine what the order of transactions is. Most of the world's computing power is in personal computers, so it is at least somewhat fairly distributed.

In theoretical terms, wealth can be turned into hashrate. In practical terms, most of BTC is mined on dedicated mining rigs by a relatively small number of players.

I don't think this is correct. The book "The Blocksize War" by Jonathan Bier does a good job of covering this topic.