and I think the set up of the question gets a bit complicated. How you want to call these things is a little loaded.
Do heroes like Thor or Superman have to try? There are instances of them going further than nearly anybody. Thor against the Celestials or Galactus and so on. He has done this before and often.
That said, they are also top tier guys. In most situations they are not threatened by the more standard villain or criminal. Do they need to try or have that uphill battle their where grit alone will win the day. Hard to say that when they can win by flicking the guy on the nose.
If one consider a Batman or Punisher than those day to day guys are more of a threat. A stray bullet will do the job. Every fight they have is uphill so to speak and it is a comment on their determination and will that they can swing out of their weight classes (I am not saying Batman and Punisher are equal either, just an example).
IMO, it is not hard to point out that Thor and the like are full of whatever you want to call determination. However, not every situation demands that they do so. It is rarer that they would than other guys.
I feel conversations like this are meant to highlight the lower tier guys as opposed to poop on the higher tier guys. It is like when somebody says someone is pound for pound the strongest or whatever.
when most anyone else would quit, either because they physically can't go on or because they give up.
Even under immense odds, most heroes don't 'give up', but when they get beaten down, they may not get up where the guys with the most 'fight' or mental toughness don't.
Thor's functioning while under Hela's curse is a pretty impressive example, as is both Thor and Superman's performances under Jurgens vs. Destroyer and Doomsday respectively.