All property discussions won't make sense until you separate land from capital improvements (houses). Property prices will not stop climbing if you build more houses, and in fact, land prices go up if you build more houses. Rents go down per house if you build houses much faster than increasing demand, but you can't build more land.

Supply and demand is not the issue when dealing with something of inherently limited supply, such as location/land.

If you want rent to go down, absolutely build more houses. If you want land prices to go down, tax land value.