I agree with much of what you said, but especially with this. Some people treat civs in the game as though they represent certain periods in history, while this is absolutely wrong. Civs in the game represent the entire history of the nation, not just a certain time period. It is not like France in Civ V represented the Napoleonic Empire, or Germany represented the Second Reich. I am also against splitting India, China, Germany, Indonesia etc, because a civilization is not a political entity, but the nation itself, even when talking about the USA and Brazil. This is why I hated it when they included the HRE, this is why I don't want them to include the Timurids, this is why I hate it that they call the Turks Ottomans. Having said that, I am also against the so-called "blob civs" such as the Celts and the Polynesians.
While I understand you and partially agree, I also partially disagree, for the simple reason:
Germans are a singular ethnicity which always had close language, identity, mostly being confined to one (HRE, kind of confederation) or few (culturally close) states
Americans are not a singular ethnicity but a singular identity, "civilisation", culture
India not only doesn't have but never had any singular ethnic group, language, culture, or sort of "national identity" similar to those. It has always been a subcontinent of enormous population and enormous number of big and small ethnic groups, huge variations between skin color, religions, languages, and even religion groups (muslim, dharmic, buddhist, animist) and language groups. India has always been divided between various states or regional empires. Across 3000 years of Indian history it was never unified before 1947 (well, it is not unified now, to be exact

with Nepal, Bangladesh and Pakistan being independent), across 3000 years of Indian history there was never a "confederation of Indian states" and only three empires ever before 1947 managed to unite most of (Most of! Not "the entire) subcontinent - Maurya (for few decades), Mughals (for few decades and as outside conquerors, not indigenous people) and Delhi (two decades and also not exactly indigenous).
Before modern nationalism and independence there never was an idea of "Indian state" because "India" is as big and with far bigger variation than the entire Western and Central Europe. Differences between southern Dravidan states and northern Hindustani states were far bigger than differences between Germany and Austria - yet we get separate German and Austrian civs in civ series but not separate Indian civilisations.
Regional differences between Indian regions are so big that carving few separate civilisations from it isn't any more far fetched than naming each separate European country a "civilisation". Differences between Punjab, Bengal, Gujarat and far South are as big as differences between many European countries.
That's not to even mention how different identity Sikhs, Muslims and Hindus have, and how different outside empire (Mughals, Kushans) were culturally from Hindu states like Vijayanagar.
To sum up, yes, I think that idea to make few separate civilisations from India is very legit, because India is not like (ten times smaller) Germany or <input European nation>. In fact your very use of term "nation" for India is rather inappropriate.
India is not a nation, it's more like confederation of ethnic groups connected by history and some genetic/cultural/religious identity.
>then why India unified for independence
It didn't - Sri Lanka, Nepal, Pakistan and Bangladesh went into separate ways, Hyderabad initially wanted to be independentand got forcibly annexed, Punjab and Kashmir were separate complicated issues and there were other regions unsure of Indian union. As for the rest, I don't know, but I also have no idea how would European nationalism develop if countries from preindustrial (or even feudal) era got thrown into 200-years long industrial colonialist era.
That's speaking about relatively modern India, because historical states of Muslim sultanates, Kushans, Maurya, Harappa etc etc were so wildly diverse it'd be crazy to not consider them separate civilisations.
tl;dr Smaller civilisations carved from Indian subcontinent's history are entirely legit idea, because India isn't similar to European nation at all.
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On top of that I wanted to say that various people from various "interpretations of civ series" fall into the fallacy of seeing far more regularity and sense in the way civs are created by devs than there is IRL. What I'm trying to say, it's popular video game that can't be even called 'historical' (more 'inspired by history' or 'with historical elements') and devs are adding whatever playable factions they want if they a) existed b) seem to be interesting c) would be fun to play. There is no deep philosophy behind this, not strict rules of what constitutes a civilisation and what "civilisation" means, and that's fine because very few people care about that. Some "civilisations" are based on the modern nations and their history since medieval ages (European nations), some are based on modern conglomerates (India) and consist of many sub-civilisations mixed together, some civs are not based on nations but political entities, other are based not on political entities but dynasties, other are based not even on dynasties but cultural or ethnic relations... And this will happen in the future for the simple reason: deep social science discussions "what is civilisation, what is state, what is nation, what is culture" are too complicated, messed up, unclear and controversial to be worth caring about them while creating popular video game.
Ultimately, civilisation in civ series is "historical society" and devs are going to put anything that fits this very open concept - they may divide India on 10 civs, put is next to the united India, particular German city states of HRE era, Islamic dynasties, Canada and Maori confederation, and they will do that because that's fun.