The problem with simplified controllers is that they only actually simplify things if the game itself is relatively simple. If you can only move and jump, then you only need the d-pad and a single button. But once the game is more complex, and gives you more actions than you have buttons, then the "simplified" controller just ends up pushing the complexity somewhere else. You either:
1) Start using menus to select actions, but that's no good in an fast paced game, so maybe you can let the player pick which of the six actions available they want assigned to the two buttons you've permitted them. Only now they have to remember what they assigned where and it keeps changing and is no longer simple. The system can be handy, but it's certainly no friendlier to new players.
2) Context sensitive actions. Which is a great way of allowing an unlimited variety of actions with simple controls. Except when you don't know what action is going to happen, or when you get two context areas too close and suddenly every time you try to vault the railing you end up taking cover instead. Can be great, but can be very fiddly. For example, in SSBB, if playing with the Nunchuck Only control, up is jump... and enter doors. So if you're standing by a door you can jump.
3) Combos. A way of giving the player "virtual" buttons in a way, by making it so that A+B performs a different action from either A or B. Only now you can't do the A+B move without accidentally doing A or B instead because you didn't get the timing quite right. Plus how is remembering X different combos for the limited buttons you have any easier than just remembering the unique actions of X different buttons. Another SSBB example, with a GC controller, you can throw with Z. Otherwise you have to use a two button combo to get rid of items. I know players who avoid picking up bombs at all because of the unreliability of throwing them.
4) Motion controls. Great for pointing at things, natural body movements, and waggling. Not always so great for accurate and responsive controls. Several games that have you swing the controls to attack, such as Okami on the Wii, received complaints that more conventional controls would have been simpler. And games that have you draw symbols to perform actions (Black and White, Okami, SSX Blur) are all too often too picky about drawing the symbol just right, lest they confuse if for a different symbol.
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In short, if you only need three actions, just use three buttons on the controller. But once you have more actions than buttons, too often simpler controllers would result in control systems that are more complex and difficult to learn overall.