Why would you need rent control if you had active building policies that ensured supply kept up with demand? The price of housing wouldn’t change, so there would be no need to mandate a specific below market price.
You aren't necessarily going to be able to supply enough housing in the most popular spot were construction is hard and land expensive. Instead you want create equivalent areas fast enough. But without rent control all the affluent people quickly ends up in the same space, which is hard to make an equivalent of with affordable housing.