I reckon you motivation is the other way round from what you state. Claiming to be empathetic about how people 2500 years ago are the same human beings as we are, and claiming that others miss this, is a way to oppose those who think of the world as always improving and evolving for the better. So it serves your goal, which is to dish out a humbling to all the naughty conceited moderns.
To understand the enemy is to some extent to start to love the enemy and that's bad because the enemy is bad. The idea is that you can only have empathy for certain people.
Worth also pointing out that there's also a more modern but uncommon idea that empathy towards someone or a group may weaken and shutter their own "truth" or identity stories but this is for the moment only heard in radical academia not on the street.
Generally there's also a large amount of people who don't know what "empathy" means with the ever present confusion of it with "sympathy", endorsement and alignment.
If you see value in travelling to other countries and appreciate experiencing the different human cultures there, you should also appreciate experiencing human cultures from the past.
They are separated from us not by distance but by time which makes it harder to experience their culture.
So much was lost that we can only get glimpses on how lives were back then. So anything that expands our knowledge on the variety of human beings experiences is worth it.