No, printed iron sights are fine. AWCY developed some universal printable iron sights, which apparently work really well.
To add to that: Tommy guns were hella expensive back in the day. The NFA tax stamp that everyone knows and hates was set on the price of a new Tommy gun, $200 dollars, which back then was the equivalent of $4,000 dollars, hence why they didn’t see mass deployment in either law enforcement or the military.
As an aside, a lot of people seem to presume that bloated police budgets have been a staple of American law enforcement since forever, but that only really goes back to the aftermath of 9/11. Before then it was a case of you’ll get what we give you and you’ll like it! in terms of equipment, including firearms.
Drum magazines in general are known to be of questionable efficacy. It’s why most LMGs are belt-fed and not drum-fed.