Bitcoin miners per se do not control Bitcoin network. They are the backbone, but the nodes ultimately decide whether they include a mined block or not. Validating blocks is way cheaper than mining them. Expensive mining process only ensures that you can't easily flood the network with bogus blocks.

Actually, no, the opposite. One of the fundamental problems with PoS is that it has no externally observable metric that a block is correct. PoW is trivially externally verifiable. This is good for decentralization. There can be no lies from the miners.