Two thoughts:
It's a bit like a reverse Lookout: weak at the start, strong towards the end. Which means that if there are genuine trashers in the kingdom, the Thrift Store loses its appeal at the end of the game.
The +Action is a true boon as it leaves room for doing something with the stuff. Got two dead Stables in hand? Off you go. Vault, Artificer, even Storyteller shine with this. Cellar just got better than Warehouse. Are you a Hamlet idiot? Not to be worried anymore, ready yourself for the final turn with lots of buys.
Sounds like an argument in favor of the card to me, no?
It was rather an attempt at a "works with" synopsis. I fear that it wouldn't fill up with decent trashers in the kingdom, as most of your junk would go to the trash rather than the store. My fear is that it would be rather situational, less situational than Pirate Ship or Counting House maybe. But keep in mind that a 4 token Pirate Ship rewards you every time it's played, the Counting House gives you $5 or $6 once in a while, whereas Thrift Store only treats you once in the game, unless your opponent comes first.