You would lose money attacking the proof of stake Ethereum chain also. Dishonest validators get their ETH slashed.
This of POS as a voting system. currently only 10% of the supply is supporting the transition to POS and end of POW. we probobly will end up with 2 coins. Ethereum POW, Ethereum POS.
If that happens we all know who will win and I hope it ends like that if the devs really want to move to POS,one of those coins will be called Ethereum 2.0 inevitably but not for long as if they are divided one coin in POS and the other in POW we all know the lot of flaws in POS coins and most probably the POS version will end up in the trash pretty quickly.
I never thought of this scenario which I am liking and this should be a great problem solving regarding mining and moving to POS.