As for monopolies, in the UK at least the AB probably has the most (theory) exam entries with Trinity running a close second and both cover very similar content, as would be expected. So it's more of a duopoly.
Exam entries have nothing to do with producing well rounded musicians, that is the role of the pedagogue to offer a well rounded musical and instrumental curriculum!
There are so many examples in the real world where musicians who hold a specific grade/diploma are useless at musicianship skills etc and they cannot teach and certainly don't possess the knowledge to pass on.The theory exams of the AB/Trinity cannot hold a candle to the AP exam of the USA and the texts offered by international bastions. Do your research and check out the online courses by Steve Laitz from Eastman/Juilliard, then you can talk!