One of the big jokes about The Adventures Of Ozzie&Harriet was just what did Ozzie do for a living. I think that it was hoped that people would remember from radio and film that Ozzie was a bandleader and crooner coming up around the same time Bing Crosby did. Harriet was also a singer, but now a full time mom raising their two sons.
You have to view Ozzie&Harriet from a longer perspective. They were on radio for a dozen years before the TV series debuted in 1952. The births of David and Ricky were as much a part of our national folklore as Lucille Ball's most televised birth of little Ricky. And on radio it was known Ozzie was a musician.
It's not like there were any gags or routines on the show and Ozzie was not an idiot father being put down by his kids. Harriet certainly was an All American mom. I wish she had sung a little, she was a great singer in 30s and 40s. Just idealized family life in the Eisenhower years.
The show might have died had it not been discovered that Ricky Nelson inherited musical talent from his parents. He became quite the rock and roll king, but he could never be anything more than a good kid with Ozzie and Harriet raising him. No sullen Elvis Presley like rebellion in a Nelson.
Ricky had a string of some pretty good hits for about 10 years with a built in audience to introduce them. It added a whole new generation of fans for the Nelsons until musical tastes changed.
Change it did, the all American home wasn't playing quite so good in the counterculture 60s. But The Adventures of Ozzie&Harriet still has its place in our cultural history.