As one of the opponents states "This is a backdoor form of rent control." The irony is that the law will almost certainly drive up housing prices and kick out families at an accelerated pace. If the students are taking up even more dwellings local prices will go up even more and those poor family neighborhoods will sell off and move out sooner. The only people that are helped by this law are people who own real estate by restricting the housing supply.
Even if this plan works and drives down rents so the same families can live there how long is the zoning board willing to keep this up? When prices go up they will have to adopt another measure and then another. To keep rents below market value someone has to pay. If the families aren't subsidized by tax dollars then the regulation will have to try to impose a cost on someone. I say "try" because you can't force people to provide a service at a loss.