The reason houses are not affordable is not because the mortgage is more expensive than the rent for an equivalent unit. In fact the opposite is almost universally true. The problem is you can’t rent cheaply enough, to set aside enough of your income, to accumulate a down-payment for a reasonable property at a pace that is faster than the appreciation of those properties.

Take our situation just a couple years ago - we had a good deal on an old 2br apartment, paying a little under half our income to rent+utilities. I was saving about $1200~1300 a month towards just the house down-payment. Very respectable, I thought. But house prices were going up nearly 20% YoY. On a $400k house, which was very much on the cheaper end of what was available, that means the down-payment required is increasing at around $1500 a month. Literally every month I’m losing buying power. For perspective, when I looked recently the absolute minimum price I saw on Zillow for a unit in our area that wasn’t just an empty plot of land was $285k.

Raising taxes doesn’t work because the landlords will literally always just pass it on, plus profit margin, to the tenants. As long as there’s another tenant looking in the area, they will always fill the unit. People will just get in to a lease that’s 40, 50, 60% of their income because it’s all there is.