Ethereum has something like 100,000 validator nodes up right now with a plan to switch completely this year, summer I believe. Polkadot, while not nearly as popular/big, is already running as a pure PoS blockchain.

These validator nodes all have stake in Ethereum PoW blockchain and are worthless without it.

Polkadot is not "pure PoS" as well, but feel free to bring a citation to prove me wrong.

Your assumption is off base. Cardano has PoS, hovers between the top 5-3 cryptos. It works,and works quite well.

No, Cardano works towards a PoS, but at the moment is federated. They began from the "Byron era" (federated by the Cardano organization) and are now in the "Shelley era" (federated by the Cardano community).

https://roadmap.cardano.org/en/shelley/

> Alas, there is no PoS algorithm (who's security does not depend on PoW blockchain)

What does this mean?

It means that you validators use PoW algorithms to hold their stake (like in Ethereum 2.0) and/or write the state of the PoS blockchain on a PoW blockchain once in a while to prevent long range attacks (long range attacks = when someone steal all the keys of the validators in the genesis block, and create and equivalently long PoS with hardly any effort)

You need to quantify what that means for energy usage, as that is the main point of contention. Fossil fuels are the primary contributor to global warming as they're used now, but no one should have any problem with, say, a portable gas generator used during an occasional blackout.

You explained how this applies to ETH 2.0, how about Cardano and Polkadot?