I like the way that borders grow now by building improvements, but the problem is it makes culture kind of useless on a city by city basis. I have an idea which is that you have your hard borders that grow from placing improvements and your cultural borders which grow tile by tile from culture, like borders in civ5/6. If you settle a city inside your cultural borders it starts with +1 pop, and the AI cannot settle within your cultural borders. This would mean if theres a hole in your empires borders it gets filled it by your cultural borders, so the ai can’t put annoying cities down and encourages you to eventually settle it. If you culture bomb into your cultural borders with an improvement the culture border tiles shift outwards.
The ai also can’t culture bomb your cultural borders and visa versa, and cultural borders can’t take over other civs hard borders. Although maybe the cultural borders could clash with each other, like civ 4 but less annoying.
This is a pretty basic idea of how this could work but I think it could be interesting. It would also help differentiate culture from science since right now they both have the exact same function of unlocking stuff on trees.