"I was jolted out of the story by a thoroughly modern concept like Briseis saying something like "from Cassandra's point of view, it must have looked like..." etc. I mean, the novel goes for a blunt, timeless language in general, but to my mind, someone talking about other people's "point of view" is someone with a mind shaped in the last few hundred years."

Why? We evolved to have mirror neurons precisely to we could understand other people. It's a survival skill trying to see the other person's point of view.

Traders, leaders, wives, husbands, etc. all benefit from being able to do this.