It's really hard to do a "fall" mechanism that doesn't just kneecap the player with a bunch of annoying stuff though.
1. Buildings (or Districts, in Civ VI) that produce any kind of currency (e.g. Research "Beakers" or Production "Hammers" or Culture whatevers) could decline over time. So the decision is not to build a university or a theater, but when. The House of Wisdom in Baghdad is no longer even useful, nevermind the world's preeminent college. The Acropolis and the Globe Theater don't produce today's cultural milestones. Cities like Pittsburgh and Detroit are no longer engines of industrial power, and Venice and Tenochtitlan are no longer hubs of commercial trade.
2. Without introducing internal politics to Civ, something they've obviously steered hard away from, they could bring back the administrative costs from Civ IV that put a constraint on the size of a nation. In Civ VI, more is always better, and distance is no obstacle.
3. Cutting-edge technologies and cultural advancements should cost more, while cultures that are catching up should pay less.
4. Some technologies should be nearly "game-breaking"... until the next one... and the next one. Being the first one to 'unlock' a powerful tech should be a feat akin to building a World Wonder, but the advantage gained from it is on a timer, and if #1 and #3 above are both in effect, nobody should be getting two or three big advances in a row.
5. I know some people don't like "random disasters", but they wouldn't have to be completely random. A game like Civ presumes a certain amount of god-like knowledge and power on the part of the player, so it wouldn't be unreasonable or inconsistent for the player to have some ability to predict events that real people didn't have.
Ultimately, surviving the inevitable bad stretch of road would be part of the long-term strategy for every Civ. Everybody would have a Great Flood, or a religious crusade, or a Nationalist uprising, or a draining war, or a Great Depression, or whatever. Maybe each Civ could have an 'Achilles Heel' the same way they each have a special unit or a unique building, something characteristic of their real-world history, so when you choose to play a given Civ, you'd have some idea of which Devil is coming for you.
Anyway, I'm just thinking out loud here, but my point is that I don't believe it's an insurmountable problem.