A lot of people where work is tied to your healthcare are not independent. A lot others work so much it leave them no choice to not be sane after a while. And sometimes people can't afford the expensive tools needed to deal with lots of personal issues (tools like therapy) so they turn to the cheaper options, like drugs.
I don't think it's so shocking that not a lot of people would actually be above that bar.
I had a feeling somebody would quibble with "independent." In context, I don't think it's a high bar. If we're talking about sex workers, we're not talking about people with regular jobs so work is tied to their healthcare. "Independent" has to mean no more than an independent-minded personality; exactly the sort of person who can cope with running their own business doing something that's less socially acceptable.
Therapy is not the universal requirement for mental health that many people seem to think it is. Most people just muddle through and manage to stay reasonably sane without developing substance abuse disorders. In many cases that might not be optimal, but it's not insane or drug-addled either.
Most sex workers I've come across are not drug addled nor mentally unwell. Obviously that's a tiny proportion and not enough to draw solid statistical conclusions from, but at least it's more data than you have.