As I understand it, the government sets targets / limits for immigration, and sets goals for housing. While the latter may be somewhat informed by the former, these two goals are not mathematically linked, and if housing construction falls short of the goal, that's just treated as an "oh well, we'll try again next year" scenario. I agree that "unhinged" is dramatic, but I would say this is not very coordinated or effective.

A more direct method would be to apply hard caps to the following year's immigration numbers based on the previous year's actual measured housing completions. I think this would much more powerfully align pro-immigration interest groups with pro-housing-construction interest groups, resulting in much more home construction, whereas presently there is substantial conflict between the two (especially landowners who benefit from rising demand for scarce housing).