Tax more
Imagine progressively feeding the goose less, so as to have a greater profit margin on the golden eggs it laid. No particular percentage of feed reduction seemed too harmful, until one day it died unexpectedly.
It feels like you've left some important people out.
The systems that contribute towards A are mutually reinforcing, vicious spirals in a neoliberal capitalist world. Just like in the art world, there is no hard objective value to vacant housing, and many purchases are made on debt. It's worth whatever the last guy paid, and so the banks will loan you 80% (or more) of whatever the last guy paid. This is a form of money creation. We have collectively bid up the housing stock, completely separated from the utility value, at a rate we generally expect to be competitive to loaning real operating businesses money to invest in actual operations.
If you tax ALL of the prospective value, and price sinks down all the way to B, you can still have profitable private housing development in a steady state. Unmet demand is a thing that exists. Yes getting to B overnight probably represents a crash in your overall asset investment picture, but getting 1/10th of the way there, locally, less so. Phasing it in over time, less so. If you're expecting 5% and you get 4.5% that's still a return.
The thing about this type of redistribution is, it's just a way better more functional economy than the idea of conventional price setting with the addition of rent control, or than the status quo. Rent control tears incentive structures and makes willing landlords into unwilling landlords who are instructed to be creative in how miserable they make their tenants; Its supposed goal of affordability simply shifts costs from older tenants to newer tenants. The status quo where property taxes are very low and so A is significantly greater than B simply doesn't establish those incentives of mutually agreeable economic exchange to a great degree in the first place. "I bought a house as an investment. Rent it out? I mean... there are upsides and downsides."