"So... Should Nintendo improve the NES emulator to prevent the original slowdowns and such from happening?"
The SNES emulator would probably need it more. Tons of games for that console have slowdown. I would like the option to turn slowdown on or off. For some slowdown is part of playing the game exactly as it was. I view slowdown largely as a mistake that should never have been there but I imagine some purists wouldn't want it fixed. Plus with some shmups slowdown actually makes the game easier. If the enemies suddenly started coming at full speed someone who had already adapted to the original version would be thrown off.
I however have always wanted to play some titles without slowdown. Mega Man X without any hiccups during Armored Armadillo's stage in theory sounds cool as hell. I think it would be nice if there was an option to turn slowdown on or off. I think R-Types for the Playstation had this as an option so it's doable in theory.
Such ideas may raise costs though. I think it would good to offer two "brands" for VC games. You can get titles exactly as they were for less money or get "special edition" versions that cost more and have little touchups like saving high scores, removing slowdown, fixing translation errors, removing censorship, making arcade ports more arcade perfect, etc. Konami apparently used their own memory mappers on the Famicom but they weren't allowed to do that on the NES. So the Famicom versions of games like Castlevania III have better music. Why can't we get an NES perfect Castlevania III and an "enhanced" version with the better music as an option? If they could do Turtles in Time why not have four options: arcade, SNES, Genesis (Hyperstone Heist), and special version with all the extra content in one game?