Prices are already jacked up to an insane level compared to wages, the horse is already out of the barn: This is not going to fix the problem renters face.
A soft cap works as a ratchet. Downturns in the rental market are sticky while up turns are slow and marginalized.
It's effectively the opposite of the way things are now, with cartelized units staying artificially high through downturns and prices skyrocketing during every shortfall.