The combination of overflow & production modifier argueably do change the game quite tremendously. Whether it's a "good" mechanic is another question, but surely almost everyone would immediately notice if they were gone.
Again, I want to point out that this is my personal opinion. So, let's have a short, non comprehensive list of some rules & mechanics that many people would, in my humble opinion, not notice or care about:
(1) Warmonger penalties. Most people just ignore them by now.
(2) Agendas. They are supposed to give the AI more character & make them more lifelike. I'm pretty sure most people don't even know what the agendas of their opponents are.
(3) Having great artists, musicians & writers. Honestly? Wouldn't one great artist type be more than enough?
(4) Gossip. Often funny, but most of the time just distracting.
(5) Emergencies. Are supposed to create alliances in desperate situations. I haven't really seen them do that.
(6) Amenities, housing & food. We have 3 limiting mechanics for city growth: Amenities, housing and food. All of them basically do the same.
(7) Loyalty. The effect is that I have to conquer the capital first. That's it.
(8) Golden/normal/dark ages. As long as you have conquered your continent, it doesn't really do anything. There is a nice slingshot with monumentality that some players would miss.