It wouldn't make any technical sense to do so. 3DS is completely different hardware, Wii U has some hardware similarities but the environment in which games run is completely different (there's an OS, a bunch of dynamic linking, etc.).
Yeah, Dolphin was a Gamecube emulator and since the Wii was basically two GameCubes taped together it was very easy for it to begin supporting Wii titles.
The Wii U could run Wii games thanks to dedicated chips on the MoBo. That's why it has to switch into Wii mode. Most Nintendo backwards compatibility depends on dedicated hardware to operate. Wii and GameCube are the exception. The Super Nintendo was going to be backwards compatible with the NES but Nintendo found it too expensive.
Pedantically, I'm not sure if there are any extra physical chips on the Wii U for backwards compatibility, at least for the major bits. On the CPU side, the Wii U uses a weird triple core PowerPC 750 (aka G3) setup, even though the 750 was a) ancient and b) not designed for SMP, in order that it could be used for backwards compatibility with the previous 750 powered units. On the GPU side it does still have the old GC / Wii "GX" GPU as a separate unit, but it's just on the same chip as the modern GPU.
Rodrigo Copetti has a great article detailing the Wii architecture and how similar it is to the GCN - https://www.copetti.org/writings/consoles/wii/ - Really looking forward to his Wii U article.
The Wii U titles appear to be far more integrated into the OS. On the Wii it appears that games were run at a pretty low level [0]. Also, on the Wii, although there is an updatable system menu capable of downloading and running some small apps, the menu shown when you press the home button while in a game was included with each game as part of the SDK, not as part of the OS [1]. (The Korean version of Mario Kart Wii was found to have unused files for a Chinese home menu [2].) Meanwhile on the Wii U it is possible to launch an entire web browser and certain other apps from the home menu and still return to your running game afterwards.
Wii boots into a shell but when a game starts, it completely takes over. The menu you see when pressing the home button is not from the OS, it is called by the game into a linked library provided by Nintendo. Even shutting down the console by pressing the power off button had to be implemented by developers in order to be allowed to release.
