Per-unit rent will go down if you increase supply of housing, but the value of the land underneath will go up if you increase the amount of houses allowed to be built on said land. There's one part of "standard economics" that a lot of people forget with property, which is that land in desirable locations is of limited supply and you cannot increase its supply.

Land at the boundaries of a city is not equivalent with land in the centre, because of location value.

I do agree that #2 should stop, but be warned that it doesn't solve land values going sky-high; it actually increases land values. The solution is land value tax, a la Henry George.