I might be wrong but I think you're sort of confusing the way game multiplayer works for the local player, and for the other players they see.
If we're talking FPS games:
The local player is moved instantly based on their local inputs, and the server will also move them using the same rules. The local player will be corrected in any case where they don't match.
For other players that the local player sees, extrapolation in twitchy multiplayer games like FPSs is notoriously bad as the players are so hard to predict, so usually you have them running e.g. 100ms behind so you can (hopefully, depending on latency) interpolate between two data points from the server instead of trying to guess the future at all. So you still have the "behind real time" problem. The only reason the local player can avoid that is they have the benefit of local inputs. In an Uber sense they are the car.
Obviously that's a problem in games too, because now the player is shooting someone who's behind where they are on the server, so they miss. Latency Compensation fixes that - having the server rewind time to see what the client would have seen. But that won't help the cars-on-a-map problem.
Having said all that, I do agree with your point. Taking a couple of old data points and extrapolating from there should work pretty well for the cars problem. You'll see them snap back when they stop at intersections though.