Rent control to reduce uncertainty for people already living there isn't a lottery odds thing - it's not a solution to the problem of hard to find new places, it's a solution to the problem of getting priced out by external forces.

It has side effects, but is also addressing a specific problem people want to handle that isn't necessarily fixed by "just build a bunch of new market-rate housing."

Weakening rent control in the 90s in CA didn't prevent the current homelessness problems, so I have some skepticism around taking that even further. Pushing people who could afford marginal housing into no longer being able to afford it seems like a bang-up way to increase homelessness.

Part of the root of the problem seems to be cities that trying to both avoid densifying but also increase commercial and office space and occupancy and jobs. Either policy would be fine by itself, but they explode when put together. Some cities are slowly starting to realize this, but saying "we don't need a constant economic growth rate of X% if we don't want the feel of our city to change" may not be an easy choice for politicians to sell.