The problem is: all empires always had to face challenges when going tall and having a multicultural empire. But in Civ VI, when you conquer your city (except maybe some minor amenities troubles or loyalty issues due to neighboring cities), it's like if, suddenly, they were an integral part of the empire. Which is outright stupid. The reasons why the Roman, British or Ottoman empires stood the test of time was because, to some extent, when they brought weapons, they also brought their culture in it, making the conquered territories feel as if they were part of the empire. To some extent, of course, but it's important to notice that India still kept English as a national language due to british imperialism and cultural influence.
We need some mechanics to punish in some way wide empires. Not as stupidly as Civ V but more like Civ IV:
- The corruption mechanic was a good system to represent distance from the governmental centers. We could make something similar: each city lose 1 loyalty each 10 tiles from the Capital and the city with the Government Plaza. This way, you'll have to keep an eye on your peripheric territories and just not let them rot in the sun as you focus your attention to the other side of the Empire.
- Amenities should play a bigger role in how your cities behave too, but since Amenities favor wide plays rather than tall, it would need a rework.
- The culture system of Civ IV was also interesting. Your culture spreads and each tile had a percentage of culture. In your core empire, it was 100% your culture, but at borders it was often 50/50. Having a similar system, then basing the amenities needed on this percentage and make your cities loosing loyalty from unhapiness would be a good start.
We need mechanics to represent the struggles big empires had to stay cohesive. Governors helped that in a way (even if governors are more tailored for a tall play than wide) but we need more.