In theory. In practice space isn't that limited. As housing gets more expensive it becomes economical to build taller which brings things back down. A 200 sq meter house (not small, though there are plenty larger) could be 1 floor, or 5 floors 40 sq meters for only slightly more money. The latter can fit on a much smaller lot, and so we can fit 5 times as many people in single family houses if we wanted. (at that density public transit works well so the amount of car infrastructure needed is about the same either way, with the later only needing cars for delivery and maintenance)
You can go taller as well, but above about 5 floors the standard house construction isn't strong enough and so there is an additional cost to better engineering to account for.
or, perhaps it's that if a place is desirable, the prices are going to be unaffordable since space is always limited. Perhaps policies have nothing much to do with it at all.