I dont understand this?
Why does a Dalish or Qunari or Dwarf who embraces the herald title not make sense? I mean I understand personal takes on religion or it's institutions, but why would RP'ing a Dalish Elf embrasing Andraste or the title make no sense?
My Dalish mage run will in fact have me accepting not only the title but embracing belief in the Maker while leaving her Dalish beliefs behind. And it makes perfect sense to me headcanon wise so these types of statements confuse me.
No offense, really. 
I agree that saying that non-humans as the Herald of Andraste make no sense is a bit exaggerated, since it's pretty much canon that other races can believe in the Maker too. Given that two of the three non-human origins are outcasts from their main civilization (Tal Vashoth for Qunari and casteless for dwarves), one could even say that they have as much reasons to believe in the Maker as in their races' main religions.
The real problem is again the Dalish. Although I'm sure the game will provide the chance to play a Dalish that embraces Andrastianism (as in your case), what about those who want to roleplay a Creators-worshipping Dalish Inquisitor? Especially since canon supports paganism as the belief people would expect from any given Dalish. It wouldn't make sense for them to embrace the title.
BUT maybe the real problem is that people mistake "can't help but accept that everyone will call me that way" with "actively embrace the title". As the previously mentioned video showed, the Inquisitor can express his or her displeasure when asked about the issue. As long as there's not auto-dialogue with the Inquisitor saying "Herald this, Heral that..." every time, I think players can feel safe.
Hey, it was possible to roleplay a Hero of Ferelden that hated being a Warden, so I'm convinced there will be a way to play a Herald of Andraste that hates being the Herald of Andraste.