What would your interpretation be? Keep in mind that I'm not talking about the entirety of what each race is, only their major plot conflicts. Dwarves also have caste struggle, which I admit that I omitted before.
I would not prefer a single species choice over multiple ones for pretty much any reason. I liked Hawke a lot, but I liked her in spite of the fact that she had to be human, not because of it.
I think that BioWare protagonists intrinsically view
all "major plot conflicts" from an exterior point of view regardless of race or species and that it is up to the player to roleplay them any other way
anyway, and I think that this is a feature, not a bug. I think that experiencing most of those conflicts is significantly easier to do through the mediation of
other characters, which can be characterized in a way that the protagonist of an RPG can't, and that this would not change if the protagonist were restricted to a single race or background. I do not believe that forcing the player to play as an elf would meaningfully improve BioWare's writers' ability to convey the meaning or experience of any supposedly intrinsically elven conflicts in the setting.
I think that your particular example in the OP is indicative of this point. Hawke was neither a mage nor a templar. Even Mage Hawke wasn't a mage: she existed apart from the Circle and blood-mage communities by design, and could align herself with whatever faction she chose with virtually no consequences at all. Nothing about the way the mage-templar conflict in Act 3 was written forced Hawke into a particular position, or allowed her to experience the conflict from 'inside' either group. But people made strong identifications with the respective sides anyway.
I think that nothing we've seen from either Tevinter elven slaves or elven viddathari indicates that there is any stratum of interest in specifically elfy problems among the elves there. Granted, this is based on very limited data, and new material could change that appraisal dramatically, but the existing information
all points in the same direction. So positing a primary conflict between elves and Vints is more than a little presumptuous and silly, like proposing a Manchu national revolt in modern
Dongbei.
I view a request for a purely elf story in the next game as a complaint by the community of players who prefer to play as elves and who believe that
Inquisition failed to meet their expectations in terms of being able to be surrounded by elfiness. I think that many people in that community are bizarrely parochial and out of touch.