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Ethereum proof of stake beacon chain has been live for 6 months now: https://beaconcha.in/

That's running only a fraction of the network, though. The concerns are whether or not it can scale (or at least those have always been my concerns), and I'm of the opinion it won't work.

I hope I'm wrong.

It's not running any of the network. It's running on its own, and it's well beyond the point required for security. It reads the PoW chain, and reaches its own consensus on block hashes.

What remains is to alter the clients of the PoW chain, so that it reads the PoS chain. Then instead of choosing the blocks with the most accumulated work, it chooses the blocks chosen by the PoS chain.

That's not a big change for the PoW clients, it doesn't add load to the PoS network at all, and it's all that's needed to eliminate mining.

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