Paha, terrible answer.
That's already what Wii/Not64 are. They're not running in the Wii's "N64 mode", because that's not a thing. The GameCube and Wii are practically the same platform from a development standpoint, hence why it's possible (after a massive amount of work) for the Wii to run GameCube games in Wii mode very well. The N64 is an entirely different platform unrelated to the GameCube/Wii (and Wii U), so the Wii has to work a lot harder to get the games running in Wii mode and there's a lot of room for inaccuracies to creep in, hence the limitations in its compatibility.
Add to that that improving accuracy almost always means sacrificing speed and the emulator can't just be made more accurate because games would then stop running full speed. Any improvements in accuracy will also have to be countered with optimizations to make the emulator continue to run at full speed. Is there room for this? Well, Mupen64 is developed primarily as an emulator for relatively modern computers, of which the Wii is not one. Compared to Nintendo's effort on GameCube (see the Zelda collections), Wii/Not64 are relatively slow, so there are probably improvements to be made speed-wise, but it's worth noting that Not64 already far outstrips the compatibility of Nintendo's emulator, which is pretty much "just good enough and not a bit better".
In short, N64 emulation on Wii could definitely be both faster and more accurate, but achieving either of those (and even more so, achieving both) is difficult work. There's not really a quick fix like you're suggesting here, mainly because what you're suggesting is essentially what is being done.