By itself, no, it will not solve the problem, but it does help because it distributes the housing pressure over a larger area.
Forget the superhero approach. If you're looking for one solution to fix everything, you'll live life as a very disappointed person. There are no magical fixes to big problems - it's one small step at a time, until their compounding effect starts to chip away at the problem.
The barrier to entry is prohibitive. So many people are living paycheck to paycheck, a down payment on a home within walking/cycling distance of their workplace is a pipedream.
Even if they could, with how large cities are, it's unlikely it'll be close to where they work.
The solution is always mass transit: even a simple bus, as long as it's comfortable, reasonably fast and timely will do wonders. Trains and subway, even better.
I think that the way to settle a dispute like this isn't by shouting over the cop. Is it satisfying? I'm sure. Good idea? Never.
It's on them to prove the speeding happened, and if they can't back it up in court, it's a quick dismiss.