Did the invention of the car lead to larger living spaces? Perhaps people decided to trade time for space.

Who are these "people" you're talking about? I would much rather live close to everything and walk, bike or bus. Instead I have to have a car because work is 3 miles away, doctors are 5-30 miles away, the grocery store is 5 miles away, the nearest convenience store is a mile away. And I live in the middle of one of the biggest metro areas in the country!

I'd like to have a farm in the middle of downtown too. It isn't possible. You get more choices in the same amount of time with a car, and get more space as well. Without a car you better like the doctor withing waking distance (my family considered them quacks and has heard plenty of stories about people almost dieing because obvious things were not caught in regular visits, instead the ER had to figure them out when it was almost too late). Ymmv, I like choices.

Of course cars do take up a lot of space, but even factoring that in you have more choices in a reasonable time with a car than without.

Don't read this as me approving of cars. I understand the appeal and drive, but I hate it.

Maybe supply decided for them.