I mean, to be fair, it is very hard to have a super-soldier be "tired" in a regular way considering the "science" behind super healing. So I am not surprised that certain characters don't get the same treatment due to, well, in-universe logic. (That said I did read some fic for Steve with this trope as well)

But I think you're overall right and certain characters are more likely to be written into certain situations, because we basically stereotype the hell out of them and project "i want this iddy thing to happen" onto a character it can plausibly work with. :)