I proposed a way to revamp policies a long time ago, and it presents an opportunity for culture to be mechanically differentiated from science. The idea is to introduce XP and levels to policy cards. You gain XP on policies when you have them slotted in. Culture determines the base XP gained for your policies. When a policy levels up, you get to upgrade it by 1) adding a new ability to it, 2) strengthen one of the existing abilities, or 3) combining with a different policy. Not only does this remove the feeling that culture is just "pink science", it also elevates Civ beyond its city-builder status to become a proper empire-builder. The main selling point for Civ and other city builders is to be able to admire your work at the end of a game. In a city builder, all the infrastructure you built throughout the game is evidence of good work. Civ has that, too, but there needs to be more. You should get the same sense of accomplishment when you look at the government that you built throughout the game, but policies don't feel special at all in Civ.
This is a good point. Culture does have an interesting characteristic that it has direct effect on empire-wise development as well as municipal development. I don't yet have any detailed idea on how to do this, but I'm trying to retain this "duality" and tie it into my longing for a way to give cities more character. When I look at some big cities in the US, there are certain Civ-related keywords that I think of. New York is "culture" and "gold". Boston is "science". San Francisco is "science" and "gold". This goes beyond what districts each city has. It's not that New York doesn't have schools or good ones even, but Boston has a special status as an education hub. I like to imagine these cities have made conscious efforts over the years to achieve their special statuses, and I'd like to see that reflected in the game. I've thought about municipal policy cards, which also level up like their national equivalents, but only the culture that a city generates can be used to develop its policies. I'm not sure whether it's a good idea to give such granular level of control to players, especially when it's just a repeat of what they get to do on a more macro level.