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?
Learn English – Why does the word “emcee” exist
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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.