We can debate whether accuracy is necessary in historical cinema, but as I said with Gladiator 2 - I've often found that the movies who *do* care about authenticity the movies that care about other small details, like this one. Few care about one and are slapdash with the other.
You can/should read Emily Wilson's latest take on the Odyssey, but I'm logging on to convey my hairdresser's reaction. She was AGHAST that Nolan, with his million $ budget, gave Matt Damon ONLY 6 hair extensions. As a result, his hair did not blow around properly, & that ruined the film for her.