I believe Cunctator’s point is that both “Prince Charles” and “Princess Diana” were technically incorrect titles, regardless of whether Charles or Diana was or was not a princess. In both cases, they were just convenient shorthand used in common speech. Obviously you can’t apply technical rules to something that’s technically incorrect to begin with. If “Prince Charles” is incorrect, why would Princess Charles necessarily be any more correct?
It may have gained currency by analogy to the use of the titles King and Queen, which have a generally accepted usage because, of course, the technicalities of each King or Queen could depend on the usage in their own nation, and not even other kings might know the rules. The US governemnt wouldn’t have addresses a letter to “King Kamahameha”, though he himself used that title (and not the more specific titles of European royalty); it would have at the very least referred to him as His Royal Majesty King Kamehameha of the Hawaiian Islands (by its own rules)
You wouldn’t have properly addressed a letter to him to “Prince Charles” any more than you could properly address Diana as Mrs. Prince Charles, even though she really was a Mrs, and he really was a prince. You would however have been quite correct to address a letter for the artist-soon-to-be-known-as-Prince to " Prince Rogers Nelson" (his name at birth) or to his wife as Mrs. Prince Rogers Nelson, though neither is royalty. Perhaps more appropos, “Lawyer Malone” (the American football player) is a correct address, but though we may refer to “Lawyer Smith” in some parts of the US, as a shorthand (e.g ol’ Lawyer Smith up and died today) by analogy to Doctor, it is not the proper address for an attorney.