As you point out, increasing the skilled labour force would be a priority

Yes, and why do you think the labour force is so comparatively small right now? That's right, because it isn't lucrative enough for most people to bother with. There are so many other jobs the people can do instead.

So, to attract more workers, you need to offer them more money, and to pay them more money you are going to increase the cost of building a house. And if the cost of building a house increases, the next best alternative (used housing) is going to go up in price too.

That's how we got here in the first place. If we could pay homebuilders $1 per hour, housing would be quite affordable (to anyone not building houses, at least). But you can't. They won't show up if you try. It costs serious amounts of money to compel what homebuilding workers we have to show up, and will cost even more if you want to convince more to join them.

If the BoC manages to kill the job market like they say they will, that will change things. Building homes starts to look more attractive when you're unemployed. Taking a huge pay cut starts to look more attractive when you have no other jobs options in front of you. But, until then...