So that means if we want to solve homelessness, we need to start taxing homeless people.

Or just stop subsidizing them. In the short term, it's more suffering for the poor, but in the long run, it's fewer people born into multi-generational poverty traps and into communities where they learn to become dependent and game government programs, because the dominant source of income is unconditional social assistance programs provided at the taxpayer's expense.

You think homeless people were predominantly born on the street to homeless parents?

No but they come from predominantly poor families, and are disproportionately represented by those raised in single parent households.

So you can provide early childhood nutrition to kids, welfare to their mom, free education for the mom, free childcare, etc, to try to improve the outcomes for children raised in these households, but one of the adverse effects of that is that the economic disincentive for having a child as a single mother is massively reduced, resulting in more children being born into single-parent families. The conservatives were absolutely right about the long term effects of welfarism, as shown by 50 years of rapidly rising rates of single parenthood.