You've got a bustling metropolis on the crossroads of the world.  Trade, science, glory, stability. Everything is great.  Problem is, two of your outlying attached territories is in the sphere of influence of another empire.  They're now gaining War Support against you, you're now losing War Support against them, and the people of your city are threating riots if you don't accept a civics change.

But aren't your people happy?

Proposal: A city that is "Settled" (that is, 90%+ Stability) could avoid penalties -- War Support penalties, specifically -- for having territories in another sphere of influence because there aren't cultural tensions.  Imagine the borders of countries where groups of people or religions cross borders — France and Germany, Russia and Ukraine, India and Pakistan — when stability is high (and with accepting civics?), the members of a minority are happy and welcome where they live.  When stability is lower than 90 (with/without certain civics?), that territory instead gives rise to a separatist movement that demands their homeland's civics, or to secede outright and to join the other empire (war support and grievances).

(Taken to an extreme, one penalty of a city in revolt (<30) may be that territories in the sphere of influence of another empire may start to detach from the city and damage its functioning)