Which will tend to be less desirable areas, by definition.
One approach, of course, would be to also make existing houses less expensive/desirable. Notably, wealthy people tend to have the resources to fight efforts to do that.
Despite what many in the UK think about it "being full", this is mostly an illusion from how cramped are the parts in which the houses are allowed to go; the country as a whole is mostly undeveloped.
(There are of course other considerations, with "why did you build on a flood plain?" being one of the failure modes in the UK).
Building on farmland has national security concerns (as countries are slowly realizing), as the country ends up dependent on foreign food imports after awhile. Can't grow food effectively when there is a subdivision there instead eh?
In most high demand areas (which are the ones everyone is complaining about, generally), all the decent land (or even just 'normal' land) is already developed.
Bonus - next time around, even the flood plain land might be 'too expensive' to develop on, and folks will only be able to afford houses at the dump, or in a swamp, or the like. Yay.