One thing that disturbed me about the show was the lack of a family headed by a happily married couple. As far as I recall, the only main character in a marriage is Boss Hogg, and that's a pretty disfunctional marraige at that.
I've noticed a similar pattern for a lot of supposedly "wholesome" shows from the late 1960's and 1970's: lack of a traditional family for the main characters. See also Andy Griffith and the Brady Bunch. Where is Opie's mother? Where are the previous spouses of Mr. and Mrs. Brady? And of course, with the Dukes, where are Bow, Luke and Daisy's parents? Why are they all living with their Uncle? I'm not sure whether this was an attempt by avant guard writers to undermine the traditional family, but it sure is weird.
They never got specific with it on the Andy Griffth Show but they made it pretty plain that she had passed away.
With respect to some shows, I think the main purpose was to create a vehicle for the star rather than advance any agenda. The odd family arrangements made good comedic/dramatic material. For example, I have read that Bob Newhart wanted no kids in his TV marriage with Suzanne Pleshette, because that was not the kind of material he wanted to do.
This is the second time I've read somebody concerned about this problem. Your concern wasn't as ridiculous as the other thing I read.
"See also Andy Griffith..."
Opie's Mom passed away, hence the need for Aunt Bea.
If Andy Griffith isn't wholesome enough for you, nothing is.
Ask Barney. I'm sure he's hiding something.