Lets look at it another way.
How much of the DS' success is due to the touch screen, and how much is due to it simply having a good form factor, cheaper price, successor the the owner of the last generation, cheaper development environment, and tons of quality software?
I don't think anyone can attribute the DS' success to the touchscreen controls, even though they're arguably more intuitive and accessable for non gamers.
In the Wii's case, the Wii has none of the advantages of the DS, although it shares many of the disadvantages (crappy hardware).