Even if you disregard history, the current POTUS literally talked about concentrating homeless populations into centralized camps away from the general population.
How realistic this fear is and how probable it is, is of course debatable. But given that these people probably didn't have any positive experiences with mental healthcare and institutions and that the public discourse often describes them as analogous to vermin or disease and focuses on "removing them" rather than helping them, trusting a psychiatrist - especially if it means having to go to them, especially into a clinical environment - let alone taking psychopharmaceuticals seems like it would require quite the leap of faith.
Every state does have some form of civil / involuntary commitment, though nothing like before the 80's.
Many drugs also come with unpleasant side effects, especially if someone steals them from you and you're stuck with withdrawals. I'm reminded of one person my friend was helping who hated taking his medicine, but if he didn't, he would inevitably become increasingly paranoid that vampires were out to get him. Helping the poor guy live anything close to a "normal" life was a constant challenge.