I totally agree with you - I definitely think society fetishizes productivity and your self-worth is tied to your achievements. I think it's not just an American thing and is typical of late-stage capitalism lol.
I very recently had a situation in my own life where I had to grapple with this problem. I was about to be offered an entry-level job in a reputed firm where I live and they were pretty much ready to offer me the role on the basis of an interview I did pre-pandemic. My hyperacusis has improved but overall my ears are still pretty fragile and susceptible to flare-ups - artificial audio is still triggering and recovery is just generally slow lol. Anyway, I had a chat with this firm just to see what it would entail and I ended up just coming clean about this 'medical condition' that I have etc because I wanted to be as transparent as possible. They actually took it really well and were curious and accommodating, asking questions about how it affects me etc. I had been so prepared for it to go down a lead balloon so I was really heartened by their reaction.
Anyway, they thanked me for being upfront about it and said they would have to discuss - they contacted me later on in the day to say they would have loved to hire me but they were concerned about my condition worsening and felt that my health should come first. It would have been pretty full-on in busy office, working full-time. I actually totally agreed with them. They were super apologetic about it too. To be honest, it was a bummer because if it weren't for my health, I would have got the job. There's even a nagging voice at the back of my head that is berating me for it. But I also felt weirdly proud of myself for owning it and being able to admit my limitations and doing what's best for my health. It would have been far worse for me to not disclose, take this job on, and then miserably crash and burn.
It's so important for people know their limitations - I am aware that, in contrast, it can be good for people to go outside their comfort zones at times. But that doesn't really apply to chronic health problems like these where pushing a comfort zone can be a deadly mistake.
I don't know much about the ins and outs of the American welfare system but I can say that this sounds depressingly similar to disability welfare in the UK, where people have to jump through endless hoops and face scorn. I mean, we have free healthcare etc which is great but the disability benefits system is truly awful. This is why I'm a believer in stuff like universal basic income, although that's a conversation for another day.