Title is slightly misleading...he invented the widely used AK-47. The first assault rifle was the Sturmgewehr 44 (StG 44) invented by the Germans during WW2.
http://en.wikipedia.org/wiki/Sten
In street fighting, I can't imagine it being much worse than an AK 47 (at least in close contact)...and they cost 1/8th of an M1 Garand, so presumably a lot cheaper than what an assault rifle would cost.
The assault rifle key invention is piping gas from quite far downstream the barrel to a piston that pushes the receiver back and makes it pick a new round. So you get delayed pushback. In a submachine gun with immediate receiver recoil you either lose a lot of gas or have to make the receiver heavy.
That's also why the AK47 looks like it looks, it has a "twin barrel" part way, that's where the gas piston is.