MA don’t have a monopoly but they are the recognized governing body that is affiliated with the FIM
Anyone can run their own races and call it what they like but all MA titles are recognized officially.
If an MA National title has any more value over an AASA National title, that's ONLY due to the perception of the punters. There are CAMS-recognised State championships that have rounds run under a AASA permit.
FIM affiliation is irrelevant for non-international competition. It's waved around as a big deal, but it doesn't actually mean anything at all for your typical club day.
All of that said: I don't really get the depth of MA hate. I know they're not perfect, but I've come from the world if CAMS, who are a genuinely horrible organisation, wracked with petty politics, back-stabbing, inefficiencies, a complete lack of focus on competitor's interests, and simple thick-headedness.
Compared to them, MA look like a bunch of saints and AASA & AMSAG are essential alternatives. The rise of AASA and validation of AMSAG has forced CAMS to lift its game a whole lot.
(Sorry for continual reference to CAMS - just that all of the arguments are repeats of what was said five years ago in relation to AASA vs CAMS, and ten years ago about AMSAG vs CAMS).