I think the more interesting part is investment into a bad behavior. And that's what most PoS are trying to solve, ex. with slashing, etc.
With PoW regardless outcome you have to spend money on "work", to buy IRL electricity. And even if you fail with your attack, say 51%-attack, it still costs you some significant amount. With a _naive_ PoS you revert your attack costs on chain, i.e. you can do as many attacks as you want, you can do them even in parallel and it's going to cost you few bucks maybe of computer time.
With PoW regardless outcome you have to spend money on "work", to buy IRL electricity. And even if you fail with your attack, say 51%-attack, it still costs you some significant amount. With a _naive_ PoS you revert your attack costs on chain, i.e. you can do as many attacks as you want, you can do them even in parallel and it's going to cost you few bucks maybe of computer time.