Here’s my frame to think about whether price controls are better or worse than subsidies when you want to improve the accessibility of a good.
You should prefer subsidies funded by taxation over price controls either when the supply of what is being taxed is less important to society than the supply of the good that is being provided, or if the supply of what is being taxed is significantly less elastic than the supply of the good being provided.
An example of this in action: I prefer housing vouchers funded by progressive taxes (on wage income, capital gains, etc.) to rent control. My reasoning is that labor supply and financial investments that produce capital income are both less important than housing supply, which allows for better allocation of labor (by reducing barriers to migration), the capacity to deal with population growth, and is generally more important to people. And even though the supply of housing is less elastic in the short run, over the long run, it is not significantly less elastic.
I do think the problems with housing costs and access in large metropolitan areas tends to be more of a supply-side problem than a demand-side one, often caused by bad land-use regulation. But to the extent that we try to improve accessibility by making it easier to afford homes from the demand side, housing vouchers are the solution I prefer.