That is absolutely not true. Tokyo famously has some of the most affordable real estate of any major world city. You can buy a spacious detached home in the Tokyo area for less than in Hamilton, ON. Despite the stereotype, Japanese homes are bigger than the average in most European countries.
Montreal has had the most affordable housing of the big Canadian cities. Why? Because they have the least land restricted to single family homes. Check out this zoning map. Even now, Montreal has three times the housing starts of Vancouver.
The reason why we build shoeboxes is because we preserve single family home zoning. Super high density towers, or super low density suburbs, the two most expensive forms of housing with nothing in between. To tackle affordability, we need missing middle housing. And I totally disagree about using up space: suburban sprawl sucks. I want to live in charming medium density!