In my opinion, there are two ways to approach the number of factions... let's look at some examples...
First: Games like Age of Wonders had 12 factions in the first part, then 16+. There's no balance, but people play because of the variety, the partial uniqueness of each faction, etc. Currently, the game is dead and only a few fans remember it...
Second: The game Starcraft has THREE factions. The balance is almost perfect, and the factions are ABSOLUTELY different. It participates in all esports competitions in the world. In Korea, it has become a religion. Nine years after its release, it remains the BEST strategy game.
Personally, for me, balance and uniqueness are better than a multitude of pseudo-different factions.
There is also a third way. In Civilization (a game), for example, there are VERY many factions (clearly more than 3 or even 9), but each of them is unique in its own way, and the tactics for playing as each one are different. However, this does not make Civilization a bad game and does not cause it to fall into oblivion. So, more is not always worse.