A* isn't how you get there, it's how you decide how to get there. The output is the shortest path, and that's what you actually follow.

It's pretty similar to how people find the shortest path in an unfamiliar environment. If you're looking at a map for the shortest route to a city to the north of your current position, you probably won't spend a lot of time looking at roads going south, and you'll concentrate on road segments that get you crow-flies closer to your destination.