Dynamic price control of rents to prevent them from accelerating beyond what wages can support (existing tenants win vs potential new market entrants, them the breaks when supply is catching up to demand or cannot meet demand), tenant rights with strong local regulatory oversight, government incentives to encourage a diverse ecosystem of suppliers bringing new supply onto the market based on forecasted market demand (cost of capital, regulatory streamlining support, construction labor pipeline, etc), upzoning whenever possible to encourage density as much as reasonable.
Supplier diversity is needed to prevent use of market power to restrict new supply coming online to hold rents higher than they otherwise would be (strong evidence homebuilders are doing this current state, restricting supply to juice profitability). The rest should be self explanatory. As you said, there is no silver bullet; it is various policy measures working in concert to attempt to arrive at a desired outcome. I am not anti profits, I am anti "gouge the human for basic needs for profits."
TLDR Some profits? Okay. Too much profit? Not okay. People living in constant fear of not having a home? Not okay. Build, build, build.
(am a landlord myself, do not raise rents unless actual costs go up, reduce rents when needed by tenants, keep my profits reasonable [~%6-%10], usually no more than $100/month/door)