Gotta say this has never crossed my mind once--and it's easy enough to rationalize. It's the 23rd century, it's Starfleet, so why expect things to match up perfectly to modern military protocols. And, if I'm reading this thread correctly, the system already changed a few times over the course of the 20th century, so why shouldn't it keep evolving well into the future?
Yeah, it seems that the system changes somewhat even within the 23rd century, too. One of the examples in the OP had Spock using "able", but as someone pointed out, they were using "alpha" by the time of the movies.
Various police organizations are frequent users of phonetic alphabets as well, and there's plenty of variety there.
"We are in pursuit of a red... car, license number Eggplant Xerxes Crybaby Overbite Narwhal."