I was a project manager in the construction industry for 7 years, then another 4 in real estate investment. This wouldn't work, I'm too tired to go into it and it would take a few thousand words to even start explain why it wouldn't. In theory it could work if new construction was subsidized and price fixed on a per square foot/meter basis but free markets are the "enemy" here and there's hundreds of different inputs to consider and balance.
Simply paying people more (and just fyi, we already do this. Get a quote for a kitchen remodel in any major metro and you'll realize real quick that there's carpenters making more than mid level SWEs) isn't going to motivate young people to break their bodies, work all day in the sun and shorten the length of their careers by 10-15 years compared to a desk job. There's a ton of reasons why young people don't want to dedicate their life to manual labor (and for good reason), neither money or nor status are the sole drivers here. Its simply not a great existence and is less rewarding all around, no matter how much you make. This is sort of why I don't see the argument against looser immigration policies, as the incentives you're mentioning actually exist in those communities, but that is a whole other can of worms I'm not going to get into.