RTS, adventure, on-rail shooters or any game which has inventories or any other menu with lots of choices, for example. Also almost every first-person game, not just FPS.
Look at any PC game and see how the mouse is used. IR pointing can do basically the same. Dual analogs are clunky for any situation where lots of choices are present.
NJ5, I have to agree with you, after Call of Dutty 3 and Metroid Prime 3 I can't play shooters using the the dual analogs, even when I was playing the Wind Waker I had problems to use some items because in Twilight Princess IR was used to aim but in Wind Waker I had to use the analog. Moreover after Red Steel 2 I refuse to play any new Zelda game (for an home console) where I will need to press a button to use Link's Sword. These are two of the reasons that make me see the rumored new controller as a steep back.