Even today, the use of the bayonet is considered Dogma by those in power. It's a bit strange by modern standards, but understand that it does have uses. The FG42 was a compromise weapon attempting to comprise the virtues of the Mauser K98, Submachinegun, and Machinegun all in one weapon. To do this, you cannot ignore the bayonet of the K98, the Bipod of the Machinegun, or the compactness of the SMG. In the end, compromises like these really didn't fit into a weapon firing full-power ammo. While you got theoretical full-auto fire, it was nowhere near the effectiveness of the MG42. While you got a compact weapon, it was still longer and ungainly in comparrison. As a replacement for the K98, it would have served admirably though. In the end, the concept was reborn as the M14 which also failed before it was fielded. A practical lightweight automatic rifle firing full-power cartridges just wasn't possible in those days. With modern recoil control devices, I think it would be workable, but we've already got an effective suite of weapons in the mouse-gun caliber.
Back to the bayonet, it's comforting to a soldier to know that he has a weapon that won't run out of ammo and puts fear in the hearts of men. I sure as heck wouldn't want to get speared by a bayonet!