That same 51% attack can occur on Proof-of-Stake, except you could immediately rewrite anything and also rob legitimate nodes of their stake, for all I understand.

Momentary 51% of Proof-of-Work merely makes it possible to extremely slowly rewrite the neighboring blocks. As most Bitcoin transactions require many “confirmations” (blocks coming after the one with the transaction), the attack realistically needs a very big scale, rely on serious level of luck and, through the open ledger, it will be extremely easy to detect.