... it wouldn't be a 'classic' firearm.
You don't need receivers and metallic mechanical parts if you use electric ignition, just an electric trigger, a battery and some circuitry.
You don't need proper barrels if you can use thin standard tubing encased in a 3d printed plastic sleeve, both for reinforcing the barrel and for safety.
You don't need magazines if you can store several bullets in the barrel and make the barrels single use and swappable. Due to their flimsy construction, the barrels should be strictly one use only, having to swap barrels for a new burst.
A company called Metal Storm is already applying some of these concepts in the real world.
As for lack of precision due to the lack of rifling in the barrel... they'd still be great for urban guerrilla scenarios, and probably far more precise than UZI style weapons.
I don't think the ATF guys have thought this one thoroughly enough.