Random diversity isn't the only way to do it, but it's fine. It has zero effect on the story.
It may well have an effect on the sense of story if you have a complex setting that doesn't reflect modern society. The only reason it doesn't matter in RoP is that they've taken a complex setting and mashed it flat so now it doesn't evoke much of anything except 'fantasy' and loose associations with LOTR.
Generally, though, expecting to see modern-style diversity everywhere a story takes you would be like being a tourist who complains whenever things aren't just like they are back home. The story's there to evoke a different place, time and culture, not reflect some arbitrary notion of "what the real world looks like" from the perspective of one modern urban culture (when not even the real world looks like that everywhere, as diversity means something different everywhere you go).