Is that how rent control is done in Europe? In the U.S. at least, rent control isn't taking money away from anyone. All rent control stipulates is that for the duration of your lease you cannot raise rent a certain percentage, such as 4% a year. Not having rent control allows rents to exceed earned wages for working people and pushes them to the street sooner than it pushes them out of the city.
That's taking money from landlords, (the point of reference is what everyone would have in the absence of a policy) and results in less money available for construction than would otherwise be. In the presence of supply problems you'd have to fix that either by taking money from tenants to give to construction companies (tax funded social housing) or by relaxing rent control so that the money goes tenant->landlord->construction.
