What is the reason for having characters that you don't see on screen in a TV show?

It’s so your TV doesn’t have to have a 360 degree screen. Also, it gets the point across without actually having the character make a screen appearance. Your brain knows the difference so no need to dumb it down to that point.

I know for me, the voice of Howard’s mom on Big Bang, made me laugh, because she sounded just like my friend’s mom, and said the same kinds of things. So you don’t have to see her, because so many people have someone like this person in their lives, and they are imagining the exact person they know. If they showed the actress, and she didn’t look like the person you know, it wouldn’t be as funny, the camparison would be wrong, and some people wouldn’t even make the comparison.

With the case of Seinfeld, it is actually funnier not to see the real celebrity, because the “mocking” traits of the character are not something the real celebrity would actually say, but are rather a caricature, and that’s what makes it funny. The real celebrity is similar, but the caricature is much funnier. Instead of having a lookalike actor, it’s easier and funnier to conjure up the real celebrity in your mind, and be hilariously shocked by the things he says, which are still similar to the types of things the real person says, only bigger and funnier.

MacGuffins – see definition

From an economic standpoint, it lets the producers introduce a new character and new plotlines without having to pay an actor.

Your “Seinfeld” reference was Larry David doing the voice of George Steinbrenner. The two men looked nothing alike, but David’s take on Steinbrenner’s overbearing bravado was hilarious.

Mystery.

I remember way back to the Mary Tyler Moore show. They had a doorman that no one ever saw. He always sounded slightly drunk when he called up. “This is Carlton (pause) your doorman.” It was funny at the time.
Edit: I just looked it up and he was actually on Rhoda, a spin-off from Mary Tyler Moore.

Remember in Peanuts cartoons on TV all the adults are a Wah-wah trombone ! !

I’d be somewhat surprised eating my cornflakes in my pajamas watching Walking In The Kingdom on my Living Faith Channel to have a supernatural being suddenly manifest itself.

But what a ratings winner that would be.

Belief would skyrocket.

Pay per view would transcend itself.

Unless the appearance or non-appearance of a character is not essential to the plot.

In which case just knowing they are there and might come again is enough really.

Novelty.

Humor

Charlie’s Angels! How often did we actually see Charlie?

Wilson on Tool Time with Tim Allen was always present, but never seen, as he talked through the fence. He was not quite a conscience, perhaps more of a rational compassionate thinker.

But he was physically there.

Looking back, I think it was Bob Newhart who established the trend by footing his brilliant career on characters both unseen and unheard. His bits on the telephone with only one side of the “conversation” were brilliant and riotously funny.

Actually my earliest memory of the technique on tv was a bit by Jonathan Winters, though if you think about it there must have been plenty of examples back in the golden days of radio

Anyway, the Winters bit went something like this. “Hey joe. I see you have one of those new fangled electric knives to carve our turkey here. (Winters here imitates the whirring of the knife’s motor). “Uh watch out for your arm Joe. Oh well, it’ll make a nice paperweight”.

I think the best example of this is a subliminal one.
When Oliver Hardy gave those brief but frequent looks of despair to camera he brought us the viewer into the scene with him.
We become the character we don’t see & yet we laugh & sympathise every time…simple but genius.

On Friends you had Fat Naked Guy, who lived in a building visible from the girls. He was a frequent joke, but only shown once or twice. That was all that was required. Your imagination was able to create an image funnier than anything they could show.