Rent control is not need-based. People across the wealth spectrum enjoy the personal benefits of rent control (in SF there is no shortage of housholds bringing home several hundred thousand dollars a year who pay way below market rents on their rent-controlled apartments).
The problem with getting rid of it is that the benefits of more housing supply relative to demand would probably take decades to come to fruition. But the pain of suddenly losing rent control (for the percentage of people who actually do need it) is felt immediately. Who cares if your city will have lots of cheap housing in a decade if you can't pay rent next month?
"People across the wealth spectrum" do NOT enjoy rent control. It gets gamed and abused. The bulk of SF is rent controlled, resulting in more and more people cramming into places that don't get maintained and they're not able to move out of when situations like their job changes. This is a disaster, nobody can move to be closer to work. Only a tiny amount of market rate housing is available for new residents which is disproportionately high because the rest of the market is severely under-priced.
You will never stop everyone from getting priced out. That is just the nature of things, but you can save a lot more people that pain than we do now due to foolish policies like rent control and awful zoning.