I have to be honest, I'm not really certain how playing a Qunari in Tevinter would work. I mean, Tevinters are already suspicious of Qunari, so even playing a Tal-Vashoth or Vashoth would be pretty difficult. Likewise elves don't get along very well there either. They're either slaves or hostile Dalish, from what I understand, so playing as one of those two races I feel would be like wearing a giant target on your back all the time. It would be impossible to get anything done.
Dwarves and Tevinters get along quite well from what I understand though. You could probably play a dwarf with no problems.
Anyway, the main reason why I'd want all these different backgrounds is because there's all these places and cultures in Thedas that we don't get to really experience outside of just companions. Zevran is the only companion from Antiva, and Isabela is the only one from Rivani, but these two defiantly don't represent their countries of origin as a whole. Isabela doesn't really bring up her home at all.
It might be fun to have two races that you can play with multiple backgrounds that you can choose from. This is all for the sake of immersion of course; I totally understand why people prefer more races. I love having lots of races as well, I just wish there were ways we could have them with backgrounds other than "I'm from Ferelden/the Free Marches". Playing a mage who is from a nation that doesn't acknowledge the Chant of Light where seers get possessed by spirits on a regular basis and you're in a position of respect and honor instead of fear (majority of southern Thedas) and terrified obedience (in the case of Tevinter)- sounds AMAZING to me! It would be so fun to have dialogue with companions where you basically go "Oh, is a Harrowing where you let yourself get possessed? That's cool. My first time I found a spirit of Humor!" not realizing that a Harrowing is literally the exact opposite of what they did as a seer.
I totally get what you're saying. Even though it contradicts canon, at one point I headcanon'd that my Qunquisitor was raised by an Avvar tribe, which helped explain her affinity for Rift magic and her acceptance of Cole.

But I think my only issue is that it makes it feel like humans are the only ones with multiple cultures..? Like, I'd kill to be a dwarf from Kal-Sharok or one from Tevinter's underground embassy ("I'm technically not dirty surfacer scum!!1") because those experiences would be so different from growing up in Orzammar as a noble or casteless, or even as a scrappy surface dwarf. I don't know, I just feel like in a setting that goes out of its way to show that non-humans aren't a monolith, it seems a shame to focus only on the point of view of
just human cultures? Sorry if that didn't make sense.
And I definitely agree that an elf protagonist wouldn't be a stretch in Tevinter. Likely they'd get a special status in Tevinter - being a Warden or the Inquisitor allows you to bypass a lot of society's roadblocks, but you still get racist comments thrown your way. I imagine it would play out the same way in a game set in Tevinter.