Except the Motion Plus was backwards compatible with all the previous games. What you're suggesting might (unless they already planned for it) make existing games inoperable on the new, GamePad-less version. Maybe Nintendo's got a measure in place for "no gamepad" in the OS and most games. Nintendo's own releases outside of NintendoLand and LEGO City Undercover already support other controllers. But if they don't, the "remove the GamePad" suggestion is really asking them to redo well, almost everything about the system. And that's not practical considering the length of time it would take to do - it'd be way too late, and would come up short.
To me, removing the GamePad and a hypothetical dropping of the price by $100 is a short-term fix. It would sell some units, like any price drop does in its first month. But that spike soon goes away, and what you're left with is a system that's now pretty much an Xbox 360 or PS3 but with lackluster 3rd party support and (still) only Nintendo's own games to save it. It doesn't play DVDs, doesn't play Blu-rays, doesn't do online play, doesn't have an account system, only plays Mario games - pick your criticism. They will have removed the thing that IMO was the key differentiator of the platform. It'd certainly kill off Miiverse. You still had what you had before - the only bankable thing you've got left is Nintendo's own software. And that's not doing much of anything for them right now.
Wii U has a complex combination of problems simultaneously. The name, a controller no one seems to want or know what to do with, a machine that's technically inferior, lackluster 3rd party support, Nintendo's reliance on franchises they've effectively beaten into the ground (despite the new entries being great games), and abandonment of the Wii's inviting, casual-friendly remote design. They've royally painted themselves into an inescapable corner with this one. IMO you can't fix one problem without the others becoming even more evident. If you remove the GamePad third parties aren't going to pile on with new games. The system's still going to be technologically challenged against XBO/PS4, you're still not casual-friendly. It's still an also-ran.
No one understood the GamePad. Calling it a "tablet controller" is already misunderstanding what the thing is. Nintendo probably should've called the Wii U the HD-DS or DS Home as the GamePad is basically a lower-screen for your TV (that also does off-TV play). It's not a tablet and doesn't have any processing power whatsoever in it - it can't be used separately from the console. That is not immediately gettable. IMO NintendoLand had the best examples of how a 'second screen' could be extremely fun but those were mostly multiplayer-focused; there really wasn't/isn't a 'justification' for it in solo games except acting as the lower screen, DS-style. Pikmin 3 comes the closest but despite everyone screaming that Nintendo should make a new Pikmin game it didn't sell consoles or sway anyone's opinion. It still got the "doesn't justify the gamepad's existence" reviews. :|
To me there is no fixing Nintendo's situation with Wii U. The changes they could make, IMO, wouldn't have meaningful impact or might even be more detrimental. You can't go two Christmases with sales this abysmal and make a comeback - retailers have limited shelf space, PS4/XBO are stealing the attention, there's no saving it. Best to support what market you've got with software, keep the 3DS success going. Suggesting there is a way to "fix" Wii U is futile. With software they maybe can eke some blood from this stone but it's already sunk, sadly.