I haven't always found this to be the case. There's one particular webapp we use at work that involves a lot of clicking on things, often alternating sides of the screen. With a mouse I have to mouse back and forth across the screen, with a touchscreen I can just touch the links. It's one of the few cases were I've actually preferred having a touchscreen. And I voted leaning against.
One could argue it's a workaround for a poorly designed website though.
So, replace every computer in your office... or fix the broken app.