So I encountered the word "emcee" in written form for the first time this week and was surprised to find that it was not simply written "M.C." (short for Master of Ceremonies). Why does the "emcee" form exist?
Per @Sarah's answer in this related question, the coinage vocologue was proposed for such words over a decade ago. But it seems to have no currency as yet, and personally I much prefer acronomatopoeia as suggested by ELU's @wim in a comment to that question.
There aren't actually very many in common use. By far the most common is okay, which one of a very few where the longer "phonetic spelling" form occurs more often than the short form (possibly because people aren't sure whether "ok" should be in capitals or not, and they're not sure what it stands for anyway).
A couple more where we very often see the longer form are emcee (MC, Master of Ceremonies)) and Dubya (ex-president George W Bush).
Others, such as teevee (TV, television), deejay, (DJ, disc jockey), See-Threepio (C-3PO, Star Wars robot) are easily understood, but the spelled-out versions aren't as popular as the initialisms. I assume people calling themselves dj Pee Tee, dj Jay Kay, etc. are bored with "deejay", but still like using the technique on their own names.
Turning to OP's specific question (why does the "phonetic spelling" form exist at all?), I would say okay is a special case for the reasons given above. I think for the rest, it's a mild form of "linguistic subversion" (cf Old Skool, honest injun, Windoze, k.d. lang, etc.).
Effectively, we like them because they suggest we're part of a "counter-culture", kicking against the bland orthodoxy of correct spelling and grammar. That's why they rarely become dominant - if they did, they'd no longer have the slight "edginess" that justified using them in the first place.
Hip-hop and rap is characterised by creative lyrical wordplay, and in addition to abbreviating master of ceremonies -> MC -> emcee, you'll see disc jockey -> DJ -> deejay.
Another important part of hip-hop is individuality and rejection of the status quo. Putting all this together may explain how new generations have changed and switched it up to end up with phonetical spelling.
Fluther.com answers to this question include this from CyanoticWasp:
Well, we know why the shortening happens: it’s a natural enough thing in our language to shorten phrases into acronyms that there’s surely no surprise there.
Maybe the progression from there is that the acronym becomes so successful and well-accepted that people start thinking of the acronym itself as the word. For example, a lot of younger people don’t know the term “Master of Ceremonies”, but they do know “MC”, and they think that is a word: emcee, that means “the guy who sort of runs the show on stage”.
It is entirely possible that the current generation is unaware of the original words, only learned the abbreviations and decided to make them into words. There is info on wikipedia to support this for MC and deejay has a completely different meaning than what we (oldsters) think of as a disk jockey per the wiki entry.
And roundsquare says:
I agree with [CyanoticWasp and Kayak8] that this is a generational thing. However, I think it might also just bee that each generation likes to change things up. At some point, someone made a decision to write “deejay” and it caught on. It probably came about as a current style but may eventually become all people know.
We can see more of this kind of wordplay in Eric B & Rakim's "I Ain't No Joke" where emcee itself is spelled out in letters:
The E-M-C-E-E don't even try to be
One online dictionary I consulted said:
Origin: 1930s (originally US): representing a pronunciation of MC
Considering that the letters of the alphabet have phonetic pronunciations (in other words, em and cee are already in the dictionary), it's not hard to imagine how MC would therefore be spelled emcee.
In addition to several points made already as far as acronyms becoming so widely used as to be words in their own right, use of M.C. could easily be confused with post-nominals. For example, the sentence:
John Doe, M.C., called the next act to the stage.
M.C. looks like a post-nominal (think M.D., Ph.D., or in countries with orders, you'll find things like KBE, OBE, etc. More here.).
Making a separate word for such a common title is, as mentioned, reasonable, and at least as a side benefit it avoids confusion with such post-nominal letters.