Price controls are great for incumbents, but suck for new-comers or even incumbents who want to move. Disabling price as the allocation mechanism does nothing to address the supply/demand problems, and necessitates alternative allocation rules (waiting lists, insider connections, fit/need-based, lotteries) which all have their own problems.
In the Netherlands the average waiting time for rent-controlled social houses in popular places like Amsterdam and Utrecht now exceed 10 years.
If the rent increase has been determined by market conditions to be 10%, incumbents have their rent increased by 40% of that, so 4%. And it's not asymptotic. If the rent increase next year is 0%, the incumbents still pay just 104% of the basis rent.
Over time, incumbents have unbeatable rent and can't afford to move, and newcomers pay an extortionate amount, which is the present status quo. The Swiss also blame the newcomers for raising the rents, even though they are the victims.
In the Netherlands the average waiting time for rent-controlled social houses in popular places like Amsterdam and Utrecht now exceed 10 years.