There's a difference between an emulator and running something natively that I should address here.
At it's core, an emulator tries to use software to mimic and older system/console it has nothing in common with (different architecture, parts etc.). Though this allows one to play older games on newer devices, this takes a toll on the CPU, meaning that things often do not run unless the newer system is significantly more powerful than the older system. The 3ds is only a slight step above the DS, meaning emulation on it would be extremely difficult. It would lag, chug, and have an extremely low compatibility list. Atm, the now dead 3desmume can only play 1 game at a playable state, and that's Yoshi's island ds, and even then it runs at a super low framerates without sound.
Next there's natively running game backups, which
nintendont for wii and twloader use. Essentially, you're simulating a game card/disc being inserted into the machine. The upside is that games run at near perfection, with little to no graphical glitches/ slowdown. On Wii with
nintendont, there were no downsides, since simulating a disc being inserted is very easy to do by the nature of how they work. DS cartridges on the other hand are a special case. In simple terms, when you run a DS game, and it asks for a file, say the Sprite of Pikachu, the code doesn't just say "load the pikachu file". It says "go into the cartridge slot, go here, find Pikachu, and load it". This makes things significantly harder, since the file loading itself needs to be patched. This leads to a lower compatibility list, and minor stuttering. The DS mode on a 3ds also has a low sd card read/write speed, therefore increasing stuttering and load times. It's amazing frankly twloader exists at all. Anyway, hope this cleared things up about DS emulation.
EDIT: Also, the reason flashcarts don't have this issue is complicated, but they have their own patching software that speeds things up by a huge margin. Also, since it's actually in the cartridge slot, nothing needs to be patched saying that it needs to be loaded from the cartridge slot like sd loading.