i think it's more accurate to say that a tiny percentage want to be homeless, and a slightly larger percentage only want to be homeless when their chronic mental illness or serious addiction is particularly elevated; they will need support to stabilize their lives more than once.

and typically, even the tiny percentage actively choosing it likely also have chronic mental health issues but have created a functional life for themselves. example - i knew a former vet some years ago who chose to remain unhoused. he had a lot of skills and worked off and on as needed. he also had some paranoia/delusions. he had autonomy over his life and felt safer the way he lived.

i think part of the problem is that the process of seeking services can be so slow and brutal, so it's just easier not to bother. while my city has nationally recognized support for people experiencing homelessness, it also involves as much as a month of sleeping outside with others who may not be safe or stable yet, and being certain places and certain times every day during that wait. some feel safer and better able to meet their needs on the street; honestly, for some they're right.