Willingness to work has always been and will always be irrelevant, the real question is whether you have the necessary skills to be employed productively or not. And the number of people who fail to meet that threshold is larger than you think, because American work culture dictates that people must ALWAYS "earn" their living, even if their labor is slow and inefficient and the products they make are unwanted, and we would really be better off paying them to stay home.

Also, being willing to work hard doesn't necessarily make someone good, a perfect example would be all of those coal miners, whose desire to continue risking their health to mine coal might seem admirable, but is really quite selfish because the market, never mind the environment, has already dictated that it doesn't want any more coal to be mined. They and the rest of society would really be much better off under a UBI scheme that paid them to stay home and actually prohibited them from trying to get back into the coal business.