I see successful empires reach 10+ cities  before they start collapsing.

Their influence per turns goes negative which drains their entire stability.
Their cities then start spawning rebels from time to time draining their population and army.
I'm also assuming their civics get reset and are unable to enact any new ones since they don't have influence.
Eventually they lose some cities to the rebels and they finally stabilize.

Is this good as it simulates the 'rise and fall' of empires and prevents them from running away with the game.

Or should the AI react faster before it gets out of hand and liberate some cities so that their influence per turn goes positive?

Well the player on those situations usually consolidate the smaller cities by razing, the AI does not know how to tacticaly raze, and I haven't seen them absorbing cities into bigger ones either.

They probably should be given instructions on how to reduce those deficits by consolidating cities.

I have not noticed that to be a big problem. In a few of my games I see one AI get into huge negative influence. But for the most part, they perform normally - typically around 10-20% of my own influence production. (Just checked the final situation of my two most recent games and in one no AI went into negative, and the other only had 1 AI with massive influence problem)

I suspect this is highly dependent on the map size (which influences number of independent cities that appear) and their reaction to the player.

Therefore, I would wish an easy way to demote a city to an outpost - this would allow both the player and the AI to not be over city cap if they find it hurting them too much.

I wouldn't have so much of a problem if cultural devolution wasn't a feature.

What I mean by that is that the AI will balloon up, have a massive influence deficit, no be able to advance its culture (civics?), and yet the influence pressure the AI exerts due to it's size is constantly pushing for you to undo all of the progress you made by playing competently.

It's another case of the AI using kamikaze tactics to hurt the player more than it helps itself.

They even ruin their cities desperately trying to get positive stability and influence.

Look at all the pink commons. (captured city)

This behaviour of AI probably saved a playthrough or two for me. They'll utterly dominate and then suddenly drop off. I think there also might be some bug with them going from age to age, maybe losing builder culture stability? Or some modifier they should have?

Has to be fixed. Indepedent People already come and go.

It took forever for Pink to start losing/liberating Cities. They now own 12, and 2 are rebelled/liberated.

They are probably hundreds of thousand influence in the negative.

Even if they fix their number of cities problem they will be stuck in the negative forever.

Blue and Pink never recovered due to having too many cities.
0 stability for the entire 2nd half of the game.
Pink was probably at -200k influence.