A millionaire in the Swiss forest is not homeless. Choosing to live in a tent is not homelessness. To me, the term "homeless" implies a lack of alternatives. As soon as it's a choice, to see romantic sunrises or fall asleep to ocean waves or whatever, that is, if calles "homeless", to me, a misuse of the term. It's a nice life, I've done it too and loved it, but I'd not start to call it "homelessness" and place myself into the same category as the poor souls sleeping under a bridge.
Of course it's a spectrum. Some folks have been forced out of their home and are living out of a car while finding a new place. That's homelessness. For some of those, it's temporary. For others, it's a spiral into misery, next is to lose the job, having a mental health issue, soon the car breaks down, and eventually they are sleeping under a bridge. Insubstantial of whether it's in SF, Berlin, Sao Paulo or Tokyo. Similarities to a concious choice are only superficial. Once it's a choice, it's outside the spectrum and is doing the fight against homelessness a disservice.