They already hire a specific team to do that for each region. The voice actress of Seondeok was also part of the voiceover team for Civ V and detailed the hours spent on voicework for both V and VI in an interview which Sarah Darney linked in these forums.
Specific native languages are not more accurate, as already discussed. (How could it be, given who they have cast for each leader? Only a few are deemed accurate, and many note even seeming fluent native speakers hired for the roles make curious grammar choices in their lines.)
And again, they already did specific voice over for each region, so the cost would not be prohibitive, especially compared to most modern RPGs. The entire point of having region-specifc voices is to encourage better voice acting and accuracy.
Several Koreans do know what Korean-accent French sounds like. And if they didn't, I hardly see how it would matter--the French would be listening to the French version, not Koreans to the French version. Unless said Koreans are fluent in French, raising the likelihood they know what Korean-accented French sounds like. XD
You wouldn't necessarily need an accent. See for example Age of Empires III. Not all the AI there have distinguishable accents as such (like Cuauhtemoc). And in Age II, the Saladin campaign narrator didn't have a recognizable accent as such.
For Akkadian, you could easily just glean what you can from the language and come up with something more reasonable than say, Rameses II speaking Arabic.
And yes, oftentimes ethnically appropriate actors are not the best at voice acting. As this thread is about voice acting rather than linguistic accuracy per se, my suggestion is for a more accurate, region specific approach that would make for more readily understood, historically flavorful, and flavorful characters in Civ games. Firaxis may opt in any event to continue getting "accurate" people to speak each foreign language, but I think it's safe to say most such people are bad at voice acting. Simple inflection would go a long way.
Also, I note that Augustus in Civ V had Italian-accented Latin. You can tell from the cadence.