I don't see how this is complicated. 1.2m people arrived last year, we don't know where they chose to live but they don't replace emigrated or people who have died like-for-like. It's likely that they choose to live near a city and quite naturally that's where the most pressures are being felt on schools, the NHS etc.
So in terms of houses where will you instruct Barratt to build the next 1.2m people worth of houses? Oh and by the way we need another 1.2m for next year if that's okay? It's a physical problem that creates immediate pressures every single year.
I don't really understand what else your argument proves because if people are ageing or living alone then so what? Should we shoot them instead to free up houses for immigrants?
You're taking the highest, and most unusual post-Covid couple of years on record for immigration (this year is already predicted to be back to nearer 300k net). You're making the assumption that they need a house each, but none of the hundreds of thousands that left had one?
I'm, unsurprisingly, not suggesting that we shoot old people and give their houses to immigrants. What you're doing is looking at a large problem, with many causes on both the supply and demand side, and then picking out one demand side issue, and saying that's the problem.