If you prefer more equal ownership of capital there is nothing wrong with that.
But that is completely orthogonal to solving 'the problem' of homelessness. Please don't confuse the two issues.
People are made homeless because housing costs rise arbitrarily high along with productivity. To the market, the definition of “the correct price” for housing is when there is “a little bit” of poverty.
If you happen to earn enough to land above that price then you are paying for your overpriced apartment. If you happen to fall below that line, you are homeless.
The “force” at play is a broken pricing scheme which allows/encourages landlords to continue raising prices as high as they can possibly go, which in a super high productivity area like SFBA or NYC is extremely high.
Places with less inflated housing prices had a 'homeless problem' as well until they made home a basic human right.
Hence empirically I doubt you can 'fix homelesness' by fixing the housing market. You can fix the housing market but will still have homeless problem - until you make home a human right.