Exactly, the actual disagreement is about civ design rather than historical facts, which makes this whole historical debate a bit irrelevant.
I also share your concerns regarding the inconsistency of the different civ naming (and thus design). All the more as there are strong rumors that HRE and “Abbasid Dynasty” are parts of the 4 remaining undisclosed civs, meaning we would have: English, Delhi Sultanate, Mongols, Abbasid Dynasty, Holy Roman Empire, Chinese - a terrible mix of ethnonyms, state and dynastic names. Why the hell?
Either you go for political/state names - Kingdom of England, Delhi Sultanate, Mongol Empire, Abbasid Caliphate, Holy Roman Empire, Chinese Empire - or like in AoE II you go for ethnonyms/demonyms/etc. but that would force the devs to make more precise civilisations, as for example “Holy Romans” or “Delhites” would make no sense, which means doing some historical research, something they’re obviously not into (I would go for English, Hindustanis, Mongols, Abbasids, Germans and Dutch (I’ll explain that final choice later), Chinese but whatever).
The problem with the political approach is that it inevitably leads to chronological inconsistency within the game timeframe (seemingly 5th to 16th or 17th century): the English Kingdom was born somewhere between the 9th and the 10th century, Delhi Sultanate in the early 13th century and disappeared in 1526, the Abbasid Caliphate 750-1258 (or up to 1517 under Mamluk yoke without any real power), the Mongol Empire(s) (which destroyed the latter) lasted less than two centuries (1206-1368), etc.
This is simply inconsistent, and it’s one of the reasons I prefer the cultural/ethnic approach which at least considerably reduces this chronological inconsistency. Of course the cultural approach has its flaws too but there is no perfect solution unfortunately.