Note Fitts's Law is for pointing in two dimensional space by the way; tapping is a different action. Touch occurs in three dimensional space unlike dragging a mouse. There's lots of other stuff I could say about the differences, but the main thing is you shouldn't be trying to directly calculate it in most cases. Look to Fitts's Law as a rough guide, you should really only be actually crunching numbers with it if you're doing formal research.
Also see these interesting posts about touch and Fitts's law.
Now, the reasons for the physical minimum sizes on touch screen devices are completely unrelated to the size of the screen; they're related to what you can touch with your finger with reasonable accuracy and comfort. The minimum effective size is still pretty much the same, baring other considerations. If anything position on screen (how far to I have to reach to press this button?) is more relevant than the size, as long as you meet a reasonable minimum.
As a real word example, let's look at Windows 7. Certain elements like the Taskbar are very well designed for touch; predictable location, large enough to tap without error (mostly), they work pretty well, even though they're relatively tiny compared to the size of the screen, they're usually at least half an inch wide. Even as a compact element they work well, unlike many other default UI elements; checkboxes are quite painful to work with via touch in Windows 7.
However, since you've got much more space, there's really no reason not to make the buttons physically larger on average; it's still easier to tap a 10" wide button than a 1" wide button. Determine the best control sizes based on how important the button is, how much space you need for other elements etc.
In the Windows 7 example above (and the iOS tab bar) a minimum touch size is used because these are almost always present and always in the UI so they shouldn't get in the way. Unless your app needs to make serious and efficient use of the whole 24" display your touch points should be larger on a 24" machine. How much larger? There's really no magic number. If using it feels awkward, it's probably awkward. Go by how it works.