I know that's the standard story, and certainly a comforting one. But I don't believe it, certainly not in the current economy.

More plausible is that in some cases welfare, even though it sucks, sucks less, on net, than the lives they'd be able to live working full-time at Chipotle or whatever.

Very unlikely. Also, you can only take from that system a fraction of what you can prove you put into it. So if you worked for 10 years making ten dollars an hour, you can collect for ten years, but an amount akin to 5 dollars an hour. Unless you were self employed, in which case the government gives you nothing at all because they hate you.