Houses and buildings are extremely valuable. Sure, sometimes the land is more valuable in some locations, but it still costs the average American a small fortune to build a home on it regardless of the land cost.
Still not correct. Materials and labor costs dwarf regulatory costs, even in hot markets.
The market does not inflate price, the market assigns value. In a hot real estate market, prices are value-driven, not cost-driven. In quieter markets, where supply of land is high, and builders are not booked out 1-2 years in advance, prices are cost-driven.
Artificially restricting supply seems to be the function of zoning laws and similar. If laws governing a property preclude the building of and usage as, say, high-density housing, then the supply of high-density has been restricted by regulation. Consequently, prices for property that has been enabled for high-density goes up. And because the demand for high-density housing is driven by the greater pool of demand for housing of all kinds and there's less housing overall to go around, the price of low-density housing also goes up.
I don't know what's going on in any particular place but the potential for regulations to affect supply and demand is clearly there.