"Standard economic theory is that rent control does not work, because if you force rents down, landlords may decide not to rent out their properties, which reduces the amount of rental property available."
If that's the main problem, then why not simply combine rent control with a big tax on properties rental that remain vacant for too long?
"Researchers also found that the controls helped accelerate gentrification, because some landlords demolished their older properties in favour of new-builds, which were exempt from the limits."
So don't exempt new-builds from rent control.