Because solving the issue of homelessness (or poverty in general) would mean parting with precious, precious currency.
They could do more for sure. But it's a bottomless pit. The more you invest the more "poor" people are "pulled" into orbit of the programs requiring more spend, which brings more poor which requires more spend ad inifinitum.
> I am fine with spending "other people's money" (AKA money belonging to people who don't need it)
Oh ok then, I just decided that you don't need your money and I will spend it on the poor. Since I am "good" and I have everyones best interests at heart because I said so, then there's no problem. I will also decide who does and doesn't "need" their money. What an awesome power to wield.
What weasel word language you're using "life for those with the least advantages" just because you are poor doesn't mean you didn't earn it or don't deserve it. What simplistic logic you are using, what gigantic and awesome powers you propose to wield with such little thought.