The only way to reduce homeless is rebuild traditional value and traditional family structure. Less people get divorced, less kids get abandoned. People always get last resort from the big family and the church and family friends and church friends, etc.
Get help from the government and charity organizations should be rare cases.
But we are on the destructive path for a long time. Part of it is natural consequence of social change, but it's also partly due to some people think they are capable of design a new society from top to bottom.
Afaik, most abandoned homeless kids are queers, most often trans. Then kids with behavioral issues (yes, stemming from crappy parents in the first place). I really dont understand how return to traditional values and family structure would improve either.
But there are a lot of wrinkles to this kind of thinking. What if there is access to shelter, but it imposes some kind of deal breaking restriction like no drug usage? Or no felons? Let's get even more controversial - what if the shelter bans sex offenders, should homeless sex offenders be forced to shower in libraries? Things get complicated, and a lot of politicians aren't willing to die on these hills when their housed constituents have strong emotional reactions to these things.