There's no coherent logic to wanting to split up India but not China or Persia. If I boil down your argument, it's simply: "India just feels different" which isn't true or a satisfying answer.
It's equally silly to try to lump Persia as one civ. Iran, again, has thousands of years of history, many different ethnicities, languages, and religions, etc. Same exact things that apply to India and China.
There would always be some relative change of ideologies, politics, cults, dynasties, militar organization, language or incorporation of ethnicites that anybody could arbitrarily decide to be good enough to justify a separation of civs. There is not point to question "why this one could and this one not" if you yourself dont give clear reason to put both at the same level.
PERSIA in CIV
The Persia in CIV6 have in the same civ both a Classical-Zoroastrian*-Iranian leader than a Renascentist*-Muslim-Turcoman leader, why would we expect a separated civ for another Classical-Zoroastria-Iranian leader?
We can question if the proper Zoroastrianism was official or the personal cult of Cyrus but at least in game devs decided to make it his "prefered" one. So whatever early mixed form of Persian belief Achaemenids had for Firaxis these are close enough to be Zoroastrism in-game and that is not far from the obvious fundamental role Achaemenids had in allow Zoroastrianism to mature and expand under their rule. Another close relation is the Persian (proper*) roots for both Achaemenids and Sassanians something that was exploited to challenge the Parthian legitimacy.
What about units? there are leader unique units for these. Persia in game could have Inmortals and Cataphracts with alternate leader for the same civ. We dont really need different civs to have Longbowmen, Seadogs and Redcoats when the first could be the civ UU and the others two the LUU for our favorite English Queens.
Maybe CIV7 or a later version would has two separated Iranian dynasties as civs but I would not put my money in Sassanians being so relatively close to Achaemenids especially when there are also modern muslim options.
INDIA in CIV
One India in civ has a personal name,
Mohandas Kamchand Gandhi, the figure, the meme the CIV "mascot". The story of Gandhi for CIV franchise therefore the history of Gandhi for contemporary India are the main reason for Firaxis to keep the unified India tradition. Beyond this, we can have very different civs splited-off from India:
- Magadha, representing the classical indo-aryan dynasties that were fundamental for the rise of Buddhism. Centered at Northeast India and Bangladesh.
- Tamil, representing the medieval dravidian hinduist dynasties with a naval focus. Covering Southern India and SriLanka.
- Hindustani/Gurkani, representing the renascentist* muslim turkic-eastIranian dynasties. With core at Northwest India and Pakistan.
There you have all different eras, religions, cultures, regions and thematics. For a region that by the way has more space to put theirs capitals than the closter around Mesopotamia-Iran were we would have more civs (including a possible Armenia).
CHINA in CIV
The most common suggestion about civs from China are not Chinese dynasties but cultures/peoples from what is now China. Beyond the most popular but also controvesial Tibetan civ there are few regular suggestions, the only close is Jurchen/Manchu that by the way do not cover just current China but also the Russian part of the historical Manchuria. Jurchen fit as the representative of Tungusic peoples, the only ones that actualy did something that fit the gameplay of CIV, confronting Chinese, Koreans, Mongols, Japanase, Russian and Turkic peoples, this confrontational relation with historical chinese dynasties put in context both as different. Now when people say "China is diverse so it cover anything" you are counting either the foreign invasors that were seen as barbarian usurpers or the subjugated minorities that were object of systematic oppresion, so you would be OK with civs like Haudenosaune or Lakota being part of USA because they are part of a diverse country?
If Cree can be their own playable civ then Hmong could be also, since the role as the "native civ resisting an imperial power" is not exclusive to the west.
So in resume, separated Persian dynasties are possible, that is true. But present this as the same for India or China without a proper scale and context is a disproportion.