No map shown to a driver at the detail level of navigating intersections should have to care about projections much. At that small a scale earth is approximately flat, and any half decent projection should have minimal distortions of any kind.
You can read about why projections still very much matter for large scale (which is what I think you meant; small scale would be something that shows you whole countries and not used for road navigation) maps in the article I linked. Google Maps tried out an alternative projection back when it was still Keyhole and ran into problems with angular distortion when zoomed in. The original post is sadly lost to Google shutting down their product forums, but here's a quote from a Google Maps engineer on their use of Mercator and why it matters:
The first launch of Maps actually did not use Mercator, and streets in high latitude places like Stockholm did not meet at right angles on the map the way they do in reality. While [Mercator] distorts a “zoomed-out view” of the map, it allows close-ups (street level) to appear more like reality. The majority of our users are looking down at the street level for businesses, directions, etc… so we’re sticking with this projection for now.
In the 90s, my family (inveterate roadtrippers) always kept a Rand McNally road atlas in the car. Each page had a map covering (usually) a whole state. I don’t know what projection it used—Albers, perhaps?—but I remember as a child wondering why some straight‐looking state borders were actually subtly curved.
