I haven't played through much on the heroes so far because I wanted to focus more on Babylon my first game, but both them and the societies definitely shift the core game a lot. In more ways than not, I think they basically are like mod elements - like if they wanted to create a cyberpunk version of civ without reskinning the whole game, you could find a game mode to do something like that. They certainly shift the balance of power way overboard, and I don't think are at all meant to be balanced. Same with apocalypse mode, which I never even made it through one game with. Not for me, so I won't bother.
Babylon itself, I do think they are quite unbalanced playing through them. I do love how they create such a different style to try to play them, but it's pretty insane sometimes when your neighbours are barely unlocking cuirassiers and you can research GDRs. And worst of all I seem to keep getting hit with units obsoleting on me. I was starting to build my 3 privateers to unlock submarines, when suddenly I can no longer build them because presumably I researched some random information era tech or something like that. I would certainly like to see them toned down a little so that you can't jump around so crazily on the tech tree, but would hate to take away that uniqueness that they have.
I had the same issue. I was going to build my third privateer then, without taking care, I discovered the technology for submarines. Suddenly, I wasn't able to build my privateers and get my Eurekas.
At first, I was salty. But then I laughed: games as Babylon are so random and chaotic that sometimes you're just "hey, when did I unlocked the eureka for this? I wasn't paying attention. Frack, now I'm locked..."
Or the Old gods being about Pagan cults, but no...Cuhtuluh and Vampires.... and yes I'm one of those people still salty about it, because mechanically I think both modes are very interesting, I just think the fantasy elements can be at least be given a historical or cultural flavour.
Not knowing much about Cthulhu lore to begin with I just picture them as Pagan cultists in game.
As for the vampires it seems that they take inspiration from Central/Eastern Europe and the names given to the units evoke real historical figures that were considered "vampires" such as Countess Elizabeth Bathory and Vlad Tepes. At least that's my justification for why they seem more historical than the Heroes and Legends mode.
Considering all of their relics they produce are from the Cthulhu lore that's pretty much what they are based on. The icon with a bunch of tentacles for them also kind of gives it away.
Sincerely, I know that Voidsingers are based on Lovecraftian mythos only because of the name of some relics. For the rest... Are you seriously complaining about some random guys worshipping Nyarlathotep and playing with the sanity of your citizens (something that could really and realistically happen) while you can recruit Imhotep during the Middle-Ages to help you build the Hanging Gardens in the Aztec city of Novgorod... I mean, the ahistoricity is stronger in one of those scenarios, and the cultists aren't it.
Also, the problem with tying secret societies with actual real societies (like Pagan Cults instead of Voidsingers, Freemasons insted of Owls of Minerva...) is that it's too real. I mean, a lot and an incresingly number of people consider themselves neo-pagans, so representing them as cultist driving mad populations to the point of rebellion can be seen as insensitive; and Freemasons are a real, quite influential, group of people, and representing them as a secret society might not be well-seen.
And the most compelling argument that has already been discussed: if they decide to make
actual "secret societies" (like Templars, Hashashins, Illuminati, Freemasons...) in the game instead of their fantasy counterpart, and you'd have the legions of conspiracy theorists that would come and take this to reenforce their lunacies. I'm sorry but we have already crazy conspiracists without having Firaxis giving them fuel for their fantasies.
Also, one big, gigantic advantage I feel with the actual secret societies is kind of the "international" feel they have. Except for the Owls of Minerva (which name is definitely mediterranean) and the style of Vampire Castles, every secret society feel international enough to justify any civilization to meet and join them. Bloodsucking monster existed in pretty much every mythology, lunatics worshipping chaos happened in all cultures, influential wealthy elites had their share of power in any society, and mystical scholars flourished all around the globe. With the secret societies being kind of "generic" enough, we feel they're truly fitted for any civilization. But that's just my opinion.