I guess the question is, what is the value of styling "Aids" such? My assumption is that they would say that such acronyms have become words in English, people understand "Aids" or "Nato" as a "thing" and don't even think of it as an acronym (just like "scuba diving" or "laser" or "radar").

If it has basically become a word, it just slows reading down to write it in all caps.

...but I can see it's a debatable issue. This is probably one of those things where some words will become like "laser" and "radar," and some won't. BBC is trying to be on the forefront in guessing which words will be.

The British convention has a clearer mapping between written and spoken language, but leads to ambiguity in the case where there is a name collision between an acronym and the case where there is a collision between an acronym and a common noun and the word occurs in sentence-initial position (or in title case), the latter is also a problem throughout English print usage with proper nouns (instead of acronyms), and the ambiguities that arise in print this way are very nearly a subset of the ambiguities that arise in speech with the same terms. [0]

The non-British usage has worse correspondence between written and spoken language, and leads to ambiguity where there is a collision between an acronym and an initialism, though this is probably rarer. While this may be a less-common situation than the ambiguities produced in the British usage, it is a ambiguity less-closely tied to the inherent ambiguity in speech.

Neither is "incorrect", they are simply different conventions, with different features, and either case the ambiguities produced are usually only theoretical and in practice readily resolved through context.

[0] "Subset" because the speech ambiguities occur indepedently of the conditions that affect casing (initial position in sentence, or title case); "Very nearly" because sometimes terms that are spelled identically and thus would be ambiguous in print are pronounced differently and would be distinct in speech.