There is no significant amount of federal public land sitting unused where people want to live. Only 4% of the total land in the provinces are federally owned, and most of that is parks and military bases.
The provinces themselves have some public land, but even most of that isn't in or near cities where people want to live. They could build entirely new cities from scratch in slightly less desirable locations, but that's about it.
The cost to buy private land to do this would be impossibly expensive.
It's a great concept, but it simply doesn't work in reality.