America is a group of continents that's been around for many thousands of years, Turkey is a country that hasn't.

Perhaps you meant USA. Calling people out as ignorant is always dicey IME.

Personally I don't mind the titling of historical situations using modern geographical designation as long as the head of the section tells me the historic context.

Turkey the modern political entity has control over these lands. Whatever political entity controlled them long ago is no longer relevant unless you want to get painstakingly academic.

The same goes for America where there are historical sites dating back thousands of years. America is the steward now, and it's part of the collective history of the country.