Permissioned networks are a very much easier setting to design a consensus protocol for than public ones.

Describing a consensus algorithm as "Proof of Stake" simply means it uses some kind of stake to secure its decisions, this doesn't say anything about the assumptions it starts from.

Existing "PoS" blockchains don't have the same decentralization goals as Ethereum.

From my understanding, the issue with PoS is that if a chain forks you can mine both sides without penalty. A consequence of this is that if someone wants to retroactively create a fork that starting from a block a few years ago, then people could do a few years worth of mining of this fork in an instant. And it wouldn't be possible to tell these two chains apart cryptographically. With PoW it would be computationally expensive to pull such a stunt.