An important thing to consider in evaluating what the fact that the Elizabethan/Jacobean theatre used contemporary dress for historical characters, and other anachronisms:
Theatre at this point did not have a tradition of Realism/Naturalism. There was no sense that the stage should try to accurately re-create real life. Sets, costumes, staging, characterizations -- these facets of the theatrical experience were not designed in Shakespeare's era to be an accurate reproduction of the physical world, any more than music is meant to be an accurate reproduction of human speech or of the aural world.
So the idea that there would have been any need or obligation to use period accurate dress, or to refer to accurate technology, for historical plays, just would not have occurred to them.