I think that is valid criticism. Growing up I imagined the home guard were incompetent old duffers, but as I learn more about them I realised how desperate things were at that time (1941-42) and how brave they were. Like the Volkssturm in Germany, they would have fought to the end to defend their homes. Like I said, if silly doesn't float your boat you can play the home guard serious and it would make a very interesting campaign.
All of that doesn't make the superb comic acting in Dad's Army any less funny.