the thing about the daroga in the book that i don't think any adaptation (that i've seen, anyway) has really gotten right is that leroux sets us up from the introduction that he is really amazing and totally trustwothy
so while for most of the book the characters are all suspicious of him and say he has the evil eye and whatnot, the reader benefits from dramatic irony and knows any gut xenophobic instincts they may be experiencing are wrong, because the author himself already clued us in before the story started that this mysterious man is actually good and important
(which in term sets up the overarching message of the novel later hammered in with erik about not judging by appearances, accepting outsiders, valuing the contributions of people who would otherwise be ostracized by society lest they become the very monsters we make them out to be, etc. etc. etc...)
the adaptations... don't have that initial clue-in, so for the most part they end up feeding gut xenophobic instincts. the daroga wanders around and the characters and audience both wonder who he is and what he's up to. we are given no alternative viewpoint on him except the white characters' suspicious and often racist reactions
it's at its worst when the adaptations intentionally make him more stereotypical or "exotify" him by giving him eyeliner, a menacing character design, a forced silly/sinister accent, etc. the 1991 musical is probably the least egregious in this regard, but that's really only because he's set up in his first scene as comic relief and presented as a little too incompetent to be a threat
and sure, in the end of all these adaptations we learn the truth and get the same point across--he is a perfectly trustworthy guy and, like erik, we should not be afraid of him just because he is different--but i REALLY think we miss something and detriment his character by not getting clued in on at least some of his deal from the start
honestly, if we were ever to get that perfect adaptation where he is included and portrayed as actually important, i think the only way you could really avoid this would be to:
- present the story as a frame narrative, the way the book did
- deviate from the book a bit and give him slightly more to do at the start, have us actually see him doing helpful things outside of all the white characters' sphere of knowledge so we have another perspective to draw upon. it doesn't need to reveal everything about him yet (we still want suspense, after all), but should still make it clear that he is not a bad guy, just misunderstood by the people around him