People can commute to work from areas which are currently derelict. People do not have to live on top of their place of work
You're correct, but commuting isn't cheap and since we're already talking about people having to stretch themselves/make financial sacrifices to afford to buy, then a substantial hike in their commuting costs will, in some cases, put them back to square one.
When I was made redundant last year I considered applying for jobs in London, which was feasible to commute to in terms of time, as there is obviously a much bigger employment market there. The annual season ticket from my then-nearest station, 50 minutes from London, was just under £6,000. That didn't include either daily parking or bus fare to/from the station. Just to be no worse off than I already was I would have had to get a job offering around £8k p.a. more than my previous salary, and that wasn't happening.
That's assuming there are public transport options available from the currently undesirable areas or that people have the wherewithal to run a reliable car (while still making those necessary financial sacrifices, don't forget).