Smash Bros. was built around the idea of using the Nintendo 64's control stick's ability to have gradients of directional input in a way that isn't "move in a 3D space", which created the Smash Attack and its flick based input method. The Nintendo DS doesn't have a control stick, so there's a problem. We also can't use Shake Smash from Brawl, both because the DS also doesn't have a gyroscope and because shaking the device with the screen on it would be very very awkward. Brawl did have "press two buttons at once to do a Smash Attack" for the Wii Remote but the timing needed for that input to register is annoyingly tight. Having that be the only available option for performing a Smash Attack on a hypothetical Nintendo DS Smash would be incredibly awkward. Oh, and all of these things also apply to dashing, with the Wii Remote having to use an entirely unique double tap input unused in any other way by the entire game just to get dashing to fit on something that only has a D-pad. The hypothetical Nintendo DS Smash would also have that double tap as the only available dash option. This is very unideal.
(Technically there's the Super Mario 64 DS work around of using the touch screen as a control stick. While I have no personal experience with it, I hear that this option was not well liked, and even if it was liked it would probably be worse for the frentic fighting game of Super Smash Bros. than it is for the untimed platformer Super Mario 64 DS.)
Control woes aside, remember that Smash 3DS is so taxing to run that the base 3DS model isn't able to suspend it, whereas almost every other piece of Nintendo 3DS software can be suspended without issue. Given this, I think to get Smash Bros to play on a Nintendo DS would require some serious sacrifice somewhere.