A similar principle works in UI design and industrial design. Rounded rectangles often just slap circle arcs on the corners—but that looks unnatural because you don't get such a shape if you bend a straight rod. In this approach the turning radius changes from infinity to a constant at one point, but the proper way is to change it gradually. Bezier curves accomplish that, I think.

Once you see this, you begin to notice it everywhere, just like with kerning. Apple used both ways on iPhones for rounding the phone's corners, iirc. Also I've been told that the principle applies to road turns: you don't want people to have to suddenly turn into the curve. (In related news, I wish a month of bad hiccups on Herman Tilke.)