It's not just ancient Rome, but every other show/movie that takes place in a past historical context outside of America. British English has long been considered to be a prestigious accent, so it goes without saying that characters or roles of power, be it good or evil, have been portrayed with an English accent. On the opposite end of the spectrum you have the stereotype of the surrendering French, which has affected numerous portrayals of the losers. Just an example would be Fire Nation Man in The Last Airbender. It's a show that takes place wholly outside of the Euro-western world, yet the loser is still given the accent of a Frenchman because the voice acting is from an American perspective. Another example would be the recently released Marco Polo series, where accents are all over the place, but Kublai himself has a noticeable British accent. Granted, the actor is actually British. It's also a matter of suspension of disbelief. Hearing a person speaking in American English in what is supposed to be ancient Rome can be quite jarring, even if it's no less ridiculous than someone speaking in British English. In shows catering to the masses which supposedly do not accept subtitles, directors rely on "accents" to relay the foreignness of the characters to the viewers, but within the scope of who is watching of course. In this case Americans.

The alternatives are of course, to just get actors of the native languages, but this is impossibly troublesome with dead languages like Vulgar Latin. You can teach the actors these languages as well, but this becomes more a job of memorizing the sounds than anything else.

In War of the Arrows you have Koreans speaking in Manchurian. Obviously the actors are Korean and don't actually know how to speak Manchurian, so it might as well be unintellible to native speaking Manchus/Xibe people, but it doesn't matter because these demographics are minute and irrelevant in terms of who is being marketed to. The vast majority of the consumer market for this film is Korean so nobody would be able to tell the difference.

Same thing with Mongol by Sergei Bodrov. The Mongolian spoken in that film is taught. The main actors are Japanese (Genghis) and Chinese (Jamukha), but it doesn't matter because actual Mongols make up a very small group of the film consumer market. There are around 3 million in Mongolia, and 10 million in Inner Mongolia. Even if they do get offended, which some are judging by a few posts I've read, the effect on sales would be minute.