You can design user interfaces that work for both, and mouse-driven systems profit from many of the UI changes that make for good touchscreen user interfaces — a clean, simple interaction design and large click targets, for example.

I don't think this is true. With a mouse, you can easily make very precise small movements, so a tiny button positioned right next to where you already have the mouse cursor (perhaps, for example, over another tiny button) is very easy to reach. A tiny button farther away is much harder to hit because you make larger and less precise movements to get there from where you were. The size of the target is not as important as its proximity to the cursor's current position.

On a touch screen, with no relative movement, the situation is pretty much the opposite: If you have tiny touch targets right next to each other, it's very hard to hit the right one, and you can't see if the cursor is positioned correctly before you click. If they're farther apart, it's easier to hit the right one, or at least harder to hit the wrong one. (And obviously larger targets are better.)