If you reverse PoS and PoW in your post, then your post would be 100% accurate and correct

Doesn't it cost nothing to attack a PoS coin? While you must use actual resources to attempt to attack a PoW coin?
Exactly, I thought attacking PoS coin is much more cost free (next to nothing) than attacking PoW coin.
You just have to buy 51% of the currency or track down majority of stakeholders and compromise their private keys. Much cost free
lots of people seem to believe this (I think it's even mentioned in Sunny King's PPC paper), but it's not accurate: you need 51% of the actively staking coin-age. That's much, much, less than 51% of the currency.
I had some ideas to help fix this, I'm working on it.