The 1920's were different times. I wouldn't go so far as to discount anything. BAR's, Thompson's, etc were sold commercially in the US. They were expensive but legal and the gangsters had the money to get them. A bayonet if nothing else is intimidating and I wouldn't put it past the police of the era or the gangsters for that matter to have them available if only for that purpose.
It would also make a heck of a sticker for alcohol barrels, stills, etc.
Now, you guys mentioned "parody". The US Government has distributed 12,000 bayonets to local police departments over the past few years. This is NOW, not the 1920's.