To your first point, the problem is that if Bitcoin somehow recovers after an attack, the steal itself would then be valuable for the attackers. In fact, they could in theory steal so much bitcoin as to pay for the whole thing. And even if they only manage to steal slightly less, they now have the CapEx for future attacks. So they could just keep coming back for seconds!
Implying the attacker would get to keep the coins. Depending on the duration of the attack, reorgs after the fact are still in the realm of possibility. If the attack continues for so long as to make a reorg infeasible... congrats, you've just become a Bitcoin miner. You won't get to do another double spend though, because for that you'd have to divert hashing power, loosening your grip on the network.
Also keep in mind that double spends are easily detectable. It's highly unlikely you'd get to cash out any reasonable amount of double spent coins, especially with everyone being on high alert. The only "steal" an attacker could hope for is that the mining rewards they received aren't nullified by aforementioned reorg.
(Edit: unless Bitcoin can mitigate the attack somehow, potentially by switching to PoS.)
I'd expect Bitcoin to migrate to a different hashing algorithm long before even considering PoS. (much to the dismay of gamers worldwide)