My point is that many households have adapted to the cheap labor - larger houses, larger gardens and so on based, larger than the owner can self-suppprt, based on the cost of labor.

Owners would have to do more themselves (thus spend time) or more money (that they can't spend consuming other things) if labor costs increased.

I'm also not arguing for limitless immigration. What I'm trying to say is that there will probably not be zero illegal immigration despite what politicians promise, at this point it's baked into the (cost-)structure of society I suppose and not painlessly undone.