But take a hypothetical continuum of unemployment benefits. At which point will your thesis that "people want to work but are unable" switch to "people aren't working because they're being paid way more to not work? The switch will probably be binary at the individual level but will look like a continuum when looking at the population level.
Individuals will of course respond differently depend on the specific contexts of their life. I think in the end a quantity that will matter will be the ratio of unemployment benefits to old job salary. Other factors such as job satisfaction in previous job will contribute to the variance.
The real problem we're going to have is people struggling to find jobs as demand ramps back up slowly in fits and starts. This whole conversation is an attempt to portray those struggling people as the problem. It is indirection, like in a magic trick. And the pedantic "well actually"s are falling for the trap.
It's a real bummer because it's definitely going to work, which is going to cause us to underinvest in unemployment insurance over time, which is going to make this even more painful than it was already going to be. It would just be nice if people could see that they're being played.