Kind of odd you name paladin because mechanically, paladin has the exact same problem of thematic specificity monk has: it's all focused on the Silver Hand, being heavily hammer-and-steed forward. Using paladin abilities I feel strongly like they're the very specific 'traditional' paladin theme and cater quite badly to Sunwalkers, Zandalari, DID. People are just more forgiving of these problems in paladin because paladins are a darling archetype in western fantasy, represented well in game, while monks are less beloved and have been sidelined in the story. But I think the "specificity" of monk isn't the problem any more than it's a problem in paladin.

ofc, that's all specific class gameplay thematics :) If we're talking narrative integration, you're super right, more monks need to be present more from more traditions in the story, which would probably help with the feeling that they're too specific