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.
My late papa joined the LDV briefly whilst waiting for his enlistment in the RAF. I have a wonderful photo of him meeting the King in his Home Guard uniform. He thought Dad's Army was bloody funny.
His elder brother was imprisoned in Stalag Luft III after bailing out of a burning Halifax. Never asked him if he thought Hogan's heroes was a laugh but then I don't recall him as being a terribly well humoured chap to start with.