You don't know what the side effects are because you don't know how an assault rifle is defined (it depends on which legislation you're talking about, there's no standard definition), and without proposing
specific things to be banned, your proposal is just virtue signalling "I don't like assault weapons [even though I don't know what they are or how they're distinguished from handguns]."
Depending on the proposal, a ban on assault rifles is likely either:
- An ineffective nothingburger, targeting features that don't matter for lethality, that can easily be removed or changed, or features that can be built or re-added in a weekend in a garage (which only affects people who shoot recreationally, and not someone planning a shooting for weeks or months like mass shooters tend to do).
- A ban on most semi-auto guns including the vast majority of handguns people rely on for every day carry and self defense.
If you want to try to have an effective ban without nuking handguns too, you have to be fairly knowledgeable about guns and machining and very specific about what you're proposing, and there are likely still holes big enough to drive a falcon nine through.
And then, if you come up with such a proposal that actually might work, you have to run the gauntlet of:
1. It's unconstitutional.
2. Semi-auto long guns are actually better for self defense than handguns, the main reasons people use handguns are that long guns are less mobile/concealable and louder.
3. What exactly are you going to do about the tens of millions of banned guns and maybe hundreds of millions of banned magazines for those guns? Confiscation? Do you want a civil war? No confiscation? Then nefarious people will have no trouble getting them on the black market.
(chimeracoder's reply is completely right, but I didn't want to take the detour of getting into the technical definition of assault rifle when it makes no difference in this discussion.)