But if one millionaire will pay (rent or mortage) more for a mansion on a hill than all the potential poor occupants of entire apartment building on that hill c

But if one millionaire will pay (rent or mortage) more for a mansion on a hill than all the potential poor occupants of entire apartment building on that hill could pay, then the developers will build just that mansion, even freed from NIMBY constraints. If so, then yes, but how many millionaires are there trying to grab up huge tracts of urban land for their own personal residences? And that's not even taking into account way that the most developers are going to have an incentive to keep rents overall high and so have an incentive keep the housing markets tight. They have that incentive collectively, but when rents are high, an individual developer's incentive is to build more apartments to rent out. Sure, building them might reduce the per-unit rent, but that developer collects more rent in total.