There's certainly a lot of policies they could bring back from previous versions that offer more trade-offs, like the old civics system. Maybe if there was a secondary policy card system, where you could optionally have a certain number of cards, but instead of being the virtually pure bonus cards that there are in the base game, they're all a much larger tradeoff. There would be stuff like slavery, state religions, etc... So maybe slavery would let you build a "slave builder", which is half the price of a regular builder, but only comes with 2 charges. However, you get -1 amenity per city while in place. Maybe to add in, the card would have to be in for a certain turn timer (ie. 10 turns? 30 turns?), and maybe the negative effect would persist for another 10 (30?) turns. So slavery would be cheap at the start, but once the initial charge is up, if you want to go back in slavery, then the next segment you are now -2 amenities per city. This would be very similar to the old civ 4 drafting while using nationalism (which would be another likely candidate for this).
I would definitely like to see spies be able to influence city-states. Maybe not huge swings, but a successful spy mission in a city-state should convert one envoy from another civ to yours. However, the penalty, other than potentially losing your spy, would be a large reduction in your envoys.
I wouldn't mind seeing the old culture flipping of tiles coming back as well, but maybe toned down from the past. So if you have a significant influence edge on someone else, then maybe once your city has run out of its regular tiles to expand to, sometimes it could attempt to flip a neighbour tile (obviously using the same rules as the culture bomb, so no wonders or districts). Something that can happen, but is rare, but if you're pressed up against a big capital, can potentially even flip a whole city if you don't pay attention to it.