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I have never understood what stops POS algorithms from being havens for opportunistic cheating. There is no punishment for spending energy on attacking the network unsuccessfully because you are still also playing good with the majority.

In POW schemes you can only use your mining power on a single chain; in POS it seems like you can "stake" every competing chain simultaneously.

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Ethereum's Casper uses the solution that while validator A could double-vote for multiple blocks, validator B could take those multiple vote messages, and submit them as cryptographic proof of A's dishonesty. By submitting such proof, the protocol would allow slashing A's stake, and giving some portion to B as a reward for catching them. Thus validators are strongly incentivized to only vote for one block at the end of the chain.

you can "stake" every competing chain simultaneously

This is called the "nothing at stake" problem and people have been proposing solutions for a few years but so far none of the solutions have stuck.

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