Haven't fully thought it through, but I think such a projection would be unintelligible in most cases - it would probably only look remotely 'intuitive' if travel time would always increase with distance.

For a real city, it would likely just be very weirdly morphed blobs of the map all cut up and smushed back together, with bizarrely curved roads, non-aligning roads & train lines, etc.

The more I think about this, the more I'm convinced it'll work. Somehow making the map truly dynamic by changing the scale according to the time it takes to reach the destination will be helpful. So the scale of the map changes as per the traffic and other factors that affect the time taken to reach specific destinations. This should work, yeah.