First off, race car drivers don't take turns the way they do because it's a shorter distance, they take turns in a manner which allows them to keep up their speed as much as possible, which means approaching the turn as straight as possible. If they were concerned about the shortest possible route around the track, they would hug the inside of the track all the way around.

Second, you might be able to save a few inches of travel on one particular turn, but you'd likely end up having to make additional course corrections to get into position for the next curve, thereby eliminating the fuel savings. Even if you did have perfect conditions and a perfect road, you'd likely save yourself only a few feet worth of distance.

And even assuming you are wildly successful and save 500 feet of distance on a 500 mile journey, you're talking about .018% savings. In a car that gets 30 MPG, that's .003 gallons of gas, or roughly 3/4 of one cent worth of savings. If you drive your car 200,000 miles, you would save $3 in gas over the life of your car.

Ray is right about potential danger of course, but good drivers continuously scan nearby traffic, so entering a curve one knows when no cars are nearby. In that case it's fine to aim for the apex of the curve. As for gas savings, the distance saved doesn't matter, but race drivers aren't going for that; they are increasing the radius of curvature of their turn so the speed can be higher. For ordinary drivers, less braking and re-acceleration saves a lot more than 17 cents. Anyway, my 2 cents worth.

I've been known to do a bit of freestyle driving. Ignoring the lines and taking the path of least resistance just feels good. I rarely get the chance to do it on multi-lane highways, because I would only consider it if the road was completely deserted and that usually means late at night. More often, I'll do it a little on 2 lane roads. If there is nobody at all in the rear-view mirror and I have visibility to see far ahead, I'll cross the center line to smooth out a sharp curve.

Since the traffic lanes are wider than the car ; the curves could be straightened out a small bit.

If you're on a winding road, where these constant lane changes would benefit you the most, it seems unlikely that you'd be able to do consistently the necessary signaling to avoid a ticket from the local sheriff. So..... no benefit from lane changing.