Hi Tigranes, yes, we made a mod called Allow Duplicate Cultures that allows people (and AIs) to pick any culture even if someone else has selected it. The Improved AI Culture Selection mod is different. It makes it so that AIs use different rules when selecting their culture.
Basically, the original code for the game makes AIs pick their culture largely based on resources they have exploited. So, for example, if an AI has not exploited horses, they won't pick a culture that requires horses for its emblematic unit. As you can see, this will cause AIs to not want to pick any culture that requires a resource when they're transitioning from the Neolithic to the Ancient era because at that time, no one has any resources exploited. This rule causes AIs to favor certain cultures over others: Harrapans, Mycenaeans, and Nubians, because these three cultures do not have a resource requirement for their emblematic unit at all. The problem persists throughout the eras. If an AI hasn't exploited iron, they won't want a culture with an emblematic unit that requires iron, etc. The improved AI Culture Selection mod makes AIs base their culture choice on their persona instead of the resources they have exploited. A fuller description of the way the mod works is available on the download page.
If you use this mod in conjunction with the Choose Any Culture mod, you should now see a greater variety of AI cultures in your game, and AI picks match their persona, which gives them more personality.
Were you able to get the mod tool working with the Desktop App version of the .NET Runtime (I posted a picture showing which version of the .NET tool you need in my previous post to you)?
