I said “M” as in “Mancy”!
If your father is around my age (a boomer, in other words), he might have gotten that here.
There are two ways the joke can be funny.
A) The slow burn reaction of the recipient as the speaker goes on and on tediously spelling
something completely obvious (see the W.C. Fields clip above)
B) A bizarre way of spelling that baffles the recipient (see the Phoebe example above)
Like much humor, it isn’t the joke, it’s how it’s told.
And, with Phoebe at least, knowing the character has a lot to do with it. We know she’s strange and a bit airheaded.
I’d also argue the Family Guy clip uses this a bit, as it’s playing on the idea that the guy is both longwinded and full of himself. And, since it varies up what he uses for each letter, there’s some “fun” in trying to guess.
There was a fellow we knew years ago with the last name of “Morgan”, spelled Big “M”, small “organ”. 
[quote=“BigT, post:24, topic:938395”]
And, with Phoebe at least, knowing the character has a lot to do with it. We know she’s strange and a bit airheaded.[/quote]
Yeah, that one’s a pretty well-put-together joke for Friends (which is admittedly not a high bar). Each letter is a related joke:
“P as in Phoebe”: weird because you don’t reference the word when spelling the word, and also “P” doesn’t make the /f/ sound by itself
“H as in Heebie”: like E and B, this is just based off the fact that nonsense words with -eeby endings sound funny.
“O as in Obie”: like the others, except the O in her name is silent, so it’s jarring to give it a sound.
“E as in 'ello there mate” is a triple joke. It breaks the pattern of the previous ones, it’s unnecessarily different from the previous E in her name, and using 'Ello as the word is just weird.
It’s a much more complex joke than the one the OP describes, although it’s closest to what the OP describes.
Family Guy seems to think that taking a joke way too far is hilarious. I would say that there’s a fine line between hilarious and tedious, except that there’s not, it’s a fucking highway between those two, and Family Guy finds itself on the wrong side of that highway in pretty much every bit I’ve seen of it.
Via Isaac Asimov:
Jones was having difficulty with the telephone.
“Ottiwell,” he was saying. “I want to speak to Reginald Ottiwell.”
And the operator said predictably, “Would you spell the last name?”
Jones sighed and began, “O as in Oscar; T as in Thomas; T as in Thomas again; I as in Ida; W as in Wallace—”
Whereupon the operator interrupted, “W as in what?”
Asimov adds: In my younger and more stronger years, when this was greeted with dead silence, I would say with some heat, “Don’t you see? What’s the difference what the W stands for as long as she heard the W? If she heard the W…” But by that time I have to fade out under the stony glances of hostile individuals, and it would have been better to have faded out to begin with.