I'm pretty sure that you would break your hand(s) or the grip of the uzi if you attempted to "use" the bayonet in the traditional sense (i.e., a downward/upward swipe or a direct, full-force thrust). The bayonet would need to be very, very sharp in order to be effective, and bayonets don't tend to hold an edge very well.
It still looks cool, though.
This makes sense to me. When you do a bayonet thrust on a long gun you grip it like a spear.