I don't think that is accurate. If teachers were the only people with children then I would agree. But lots of other people work locally (or not) and just have to travel further if they don't get a school close to their home.
I'm sure it will make childcare arrangements easier for teachers but not for the family that lives just outside the 200m catchment area, and has to travel a mile to their allocated school.

What most worries me is that good teachers will naturally want good schools for their children and rather than relying on the same criteria as every other parent, they will get a job in one of the best schools, leaving the poorer performing schools finding it harder to recruit the best teachers.

I completely agree that addressing the shortage of places would be a better use of everybody's time.