It was common, oh, probably up 'til the 80s, for characters in TV and movies to call the operator to make a telephone call (and I don’t mean Sarah on the “Andy Griffith” show).
I don’t recall even my backwards family ever calling the operator to make a telephone call (even long distance). So, I guess the question is “Was this just a device to let the audience know who was being called, or did people commonly place operator assisted calls IRL long after direct dialing became available?”
My grandparents definitely did place calls this way. In fact, that was the only way to place a call from their house until about 8 years ago.
When I was growing up in the late 50s, early 60s, the town next door to mine had no direct dialing. If you lived there, you picked up the phone (which looked like a regular phone, except that it had no dial), and told the operator the number. If you were calling to someone there, you called a central number and got an operator, who you told the number you wanted. The numbers, BTW, were only three digits (it was a small town).
Also, until area codes became widespread, you had to call an operator for any long distance call.
You better believe that you had to ask the operator to place the call.
My great aunt had a party line for damn near forever. You’d pick up the handset to make a call and you’d be the middle of someone else’s conversation. On a party line each “party” had a distinct ring so that you’d know the call was for you. Aunt Edna’s was two short and one long (ring ring rinnnnnnngggggg). To this day my uncle, when wanting to know what someone’s telephone number is, asks “What’s his ring?”
the ability to dial direct was dependent on the local telephone company central office. Operating companies would replace or upgrade central offices all the time - but typically worked on a twenty year (or more) life span. When electronice central offices (older ones were “mechanical”) were introduced, it took about twenty years before they were commonplace. There are actually hundreds if not thousands of telephone companies out there, and not all of them have had a chance to modernize even today.