Unfortunately, higher property values go with higher rents, and lower property values with lower rents, so people are in opposition. How can we decouple them?

Rent control is one way, but has downsides. If you push too hard people will just turn their properties from rentals into condos and owner-occupied houses. And if you want to have rent control be more than a temporary delay on rising rents then it can't reset to market when people move, which gives you several-year waits for apartments.

Means-tested housing subsidies are another option. You can require developers to set aside units for people making X% of the poverty line, or the government can give housing vouchers to people who couldn't otherwise afford apartments. These programs are very expensive, though, enough that they're perpetually underfunded. This means most of the people who need the help can't get it, and those that do have very long waits first. We could just pay the full cost and expand, but when you commit the government to paying the difference between 30% of your income and the cost of housing, housing is going to get even more expensive.

We do have another option here, though, one that can make property values go up while rents go down. We should make it easier for people to expand their houses. When people put in a dormer, finish a porch, or build an addition their property becomes more valuable, and having more available bedrooms reduces the upward pressure on rents. Homeowners win, landlords win, renters win, and our cities are healthier.

[1] Current homeowners trying to buy a different house also want lower property values, but not by nearly as much since generally you sell one house to buy a new one and so they're exposed in both directions.