In my experience going car-free and moving closer can easily be cheaper. At my previous apartment (Austin, TX) I paid maybe $200 more per month in rent to live within a few miles of my work. The savings from not having a car definitely exceeded that in my case.
As for the remainder, you're making a number of assumptions that don't apply in many cases. I'm not arguing that cycling is good for everyone, just that often optimizing for driving means making cycling more difficult.
First off, not everyone has a family. I don't, so this criticism doesn't apply to me at all.
I know one cyclist who has moved his family for every job he gets. When he gets a new job, so far they've been so far away that moving was necessary even if he drove, though. (Not actually sure he cycled before he moved to Austin, now that I think about it, but still.)
I also know at least two cyclists who have lived in the same place for long periods of time. In one case I don't believe their spouse works, and in the other case I believe their spouse might drive.