What do you consider the good parts of PoW to be? (serious question)
It's a weird concept to accept but actually the really interesting and useful property of PoW is that you can provide a proof that you destroyed physical resources (provably wasting electricity) which are committed to one and exactly one interpretation of history.
Stake based systems lock or burn or manage coins, but there's no provable tether from those coins (defined only within the system) to the real world.
PoW has an undeniable tether to the real world in the form of waste.
Thought experiment:
Say there's a PoW currency A, and PoS currency B.
Alice mines A.
Now Bob wants currency A, but he can't afford to mine currency A, because he needs special hardware.
So Bob exchanges currency B for currency A with Alice. Alice now holds some currency B, and Bob is happy with A. Now the question is, would Alice see that she "destroyed physical resources" for currency B? (Yes, to Alice she had to destroy physical resources)
Later, Alice wants to transact with Charlie, who also holds currency B. She transfers her B to Charlie, that was bought using A. Would Charlie care that Alice had to "destroy physical resources" to get B? (No, that information is useless in a PoS system)
Some time in the future, currency B becomes very popular (as it's just as secure and not wasting resources like currency A). Alice wants more B too, so she exchanges her B with the masses. Eventually, currency B takes over A in popularity, and by that time, Alice has exchanged all her A for B. The question is, would Alice now view that to get B, she had to "destroy physical resources"? Would that fact matter if she continues to transact with Charlie?
There is no reason for Alice to want B, a less secure money than A which they already hold. If Alice were perfect mathematician, this exchange would never occur.
Oh, and then there were cryptocurrencies C, D and F too, but that's a different thought experiment.
If a transaction does not do this, it can be guaranteed to be insecure.
>Faster block times means she'll get her coffee sooner
Maybe. Or maybe the merchant doesn't get paid for coffee at all (because faster blocktime means more orphans)!