That's because of angles. The base you're safe on whether your foot touches it or not. When you're diving to make a catch it's because you couldn't catch it easily and safely standing up because of the angle. You're comparing apples and oranges. When you're running through a base you're running a straight line. When you're fielding a fly ball you're running a line, tracking a ball with your eyes and then when you dive you're basically ruling that you cannot run under it and it's easier to catch a ball while diving tan turning your glove upside down and catching in full stride.
Again apples and oranges. A more interesting debate is whats' the faster way to slide, feet first or head first. I've read some interestin thoughts on both. RUnning through first is absolutely faster, it's been proven in a scientific manner as well.