Chariot racing was extremely popular in the classical era too, it just became more so as gladiatorial shows went out of fashion in the Byzantine age.
But for some reason the fights in the colosseum capture our modern imagination more, despite the best efforts of a Ben Hur!
The most prestigious event in the Olympics after the early 4th century BCE was the 4 Horse Chariot Race. Peculiarly, the award went to the owner of the chariot team, not the driver, so that a wealthy woman is listed as an Olympic Winner even though she wasn't even allowed to attend or watch the Games!
I have no problem with gamifying either system, the more that is in the player’s hands the better as far as I’m concerned for these sort of 4X games. It’s just a matter of how fun and convincing the mechanics are.
On this I'm afraid we part company. Having complete control of religion, culture, and everything else in a Civilization for dozens of centuries may be a great ego boost, but it makes a supposedly Historical 4X into a Fantasy 4X for me. It also (and again this is just for me personally), makes the game too predictable. Instead of problems relating to the effects of religion or culture, all the gamer is left with are opportunities to produce the cultural attributes or religious 'bonuses' they want.
I would much rather play with the historical Problems - 'gamified', to be sure - connected with Things You Cannot Really Directly Change, like religion, culture, climate, geography (mostly - you can still dam and canal in places) rather than make them just another set of Bonuses to apply at will in each game. I've said it before, but it pretty much is my attitude towards the game design:
Religion is what happens to you and your Civ that you have to deal with, not something you can choose and manipulate at will.
- the same goes to the Culture as it changes and modifies itself throughout the game. You may be able to influence it (and/or Religion) but you cannot really 'form' it as you will. IF you could, I doubt that any nation in the world today would look or act the way it does!