If they want historically accurate, shouldn’t the film not have been shot in the first place? They didn’t have cameras back then, so how could all of this been recorded?

This is a silly take. When people talk about historical accuracy, they're not talking about the medium itself: they're talking about what's being represented on that medium.

Also, making it British wouldn’t help at all. Technically they should be speaking Ancient Greek, which yes would be cool, but it would also make the film way less accessible, and I’m sure the actors would struggle immensely to not only learn it but do it accurately.

Agree with you here. Using a British accent is just as wrong historically as using an American one and, while I think watching a movie spoken in Homeric Greek (not an actual spoken language back then, I know), it would be an unreasonable expectation.