Sure, you will always get bigger spaces for the same price - that's why they're called suburbs, but the marginal utility of space decreases pretty rapidly. There are many cities where owning a sufficiently large space is indeed affordable. In fact this describes most cities outside of SF and NYC where we're packed like sardines.
People stopped living in cities because drug and crime became rampant, and quality of life dropped precipitously. That was the instigator, and still a cultural cornerstone of the suburban lifestyle, despite the revitalization of urban America.
People were fine living in apartments rather than owning a whole building to themselves - until the environment went to shit. They had the ability to get big houses outside the city for decades but didn't take the option until their urban neighborhoods collapsed. I suspect they still are fine with not owning a large house.
And we do see this in some places, where buying a medium-sized flat in a nice neighborhood close to good schools is as desirable as a big house with a big lawn in a nice area.
If you look at suburban developments all around the country, you'll also notice an explosion of smaller houses and townhouses - places that are in many cases no larger than apartments in the city, just in upright standing form. Space is a detail to most of the population, not a core factor.
For example, in Toronto the real estate prices are sky high in the city (e.g. I've heard of just a single floor of some of those large houses in The Annex going for upwards of $800k). There are a lot of condos being built (and already built), but they are all aimed at single people or childless couples, not necessarily at families. Two or three bedroom condos are few and far between, meaning that they aren't exactly cheap.
Take a look where the most expensive houses in Hamilton or St. Catharines or Kitchener are and where the "bad" parts of town are.