And the main factor driving down payments is housing prices, which are driven by landlords. Less landlords > less scarcity > lower prices > lower down payments.

On top of that, housing cooperatives exist, which can provide the benefits of renting (lower monthly payments than a mortgage, economy of scale for repairs & construction, less financial liability for the individual) without the negative effects of a for-profit landlord. (you progressively own more of your unit over time instead of never owning any of it, you pay lower monthly rates than you would to a for-profit entity)

They even have different ownership models, which could give more choice for pricing. For instance, the non-ownership model means you pay a lower rate, just the cost of continuing the providing and upkeep of the housing, with no additional profit margin, but you don’t end up owning any of the unit you live in. But the ownership model means often paying a bit higher pricing, but in turn, getting to actually own the unit you live in, and later sell it off if you wish to move. (some cooperatives have caps on how much higher you can sell it for compared to your purchase price, others do not)

But in the end, the one thing that makes housing more expensive, that outbids cooperatives for housing, and that increases the scarcity of the market, is for-profit landlords.

The only way you get any true positive change on down payments, housing prices, or housing availability, is to completely ban all for-profit landlording.