I do also agree with @nosafeguardingadults - shelters are frequently vile, I never used them, but I was lucky I was young enough to access a young homeless persons housing scheme (which was effectively a hostel, manned 24/7 with support staff in office hours and security guards at night, but still had drugs, rape, assault, etc issues, but we DID have our own rooms and lockable doors)..
The place I lived, that put me on the path from supported hostel, to supported flat, to rented council flat... that doesn't exist any more and there is nothing out there to support young people too old for the care homes and too young to fend for themselves.
In that area (I thankfully no longer live there) those kids end up wherever the council can put them, that may be a town where they know no one, it may be one of the many b&b's that are in fact bail hostels, unmanned at night, full of addicts, theives, rapists... Sleeping in a doorway is infinitely more appealing than those places.
It is very much a postcode lottery, there is a huge degree of luck involved. I was lucky I didn't slip down the drugs addiction route, I have a very addictive personality, I avoid alcohol as both parents are/were alcoholics... I didn't make a concious choice not to take drugs, in fact I did take drugs... I just got moved to a flat elsewhere, and the person really manipulating me was moved on to another town, before the point of no return.
My first night in the hostel though.. as I was having my paperwork processed and being shown my room, a boy was being taken out on a stretcher by paramedics having tried to kill himself (spoiler, he walked back in two days later fine and dandy. Second spoiler, he killed himself 9 years later after doing 6 years for manslaughter of his abuser, getting out, getting a job and suffering bullying in the workplace when a co-worker found out about his prison sentence).
There are soooooo many issues going on with homelessness, its not an easy thing to sort, there is no one single answer, no magic wand that can be waved.
Local authorities don't have the funds, charity run efforts can only go so far, the media like to paint all homeless people as lazy shirkers who brought it on themselves, the general public pretend they can't see or typically, patronisingly hand over a coffee and a sandwich that can't be drunk because you know you wont get near a toilet for another 8 hours and are allergic to tuna mayo in any case...
We're going to see more of it though - most people and I include anyone on here who hasn't got 10's of thousands in savings, are only a couple of 'life disasters' - death of a spouse, forget to insure the house, house fire, job loss, significant injury - away from the streets. You may scoff and say 'oh no, not me' but it's true.. your lives are FAR more precarious than you would EVER allow yourselves to believe.