Narrative benefits to fame status

It would be nice if fame had another in-game purpose than masked victory points. I don't think it should have gameplay value as such. That would just intensify snowball effects and disrupt the light trade-offs currently in the game between engine building and engine harvesting.

But maybe there could be a purely narrative or aesthetic pay-off. Like a pop-up that some historian studied the known world and found culture X to be the most famous. Or maybe some suffixes to in-game titles, like Shadowhal the Great/Brave/Lesser/Maligned. Or something in the spirit of Civ VI's era timeline. Or even just to the Culture names; Empire -> Kingdom -> Duchy - etc.

Implicitly, it's an entirely cosmetic thing and has no gameplay value. But immersion is valuable too.