Not in most of my gameplay. In most of my games the AI either declares war on their neighbor or on me.
My last game was Kongo defeated Gran Colombia -- poor Simon had a bad tundra start, sandwiched between a forward-settling Georgia and Kongo. Me on the other continent as Ottoman got into war with neighboring Germany (turn 1 they said they just plain dont like me) then later in modern era Korea declared war on me because of my warmongering.
And this was just on King difficulty.
AIs will pretty commonly declare war on one another - in my experience it's rare for AIs to wipe others out, but in one of my recent games two AI civs were destroyed by a runaway Mongolia on the same continent. They also routinely capture city states, although much less often than they did in earlier versions of Civ VI.
I believe the agenda system is the reason and in the later era, the grievances penalty.
I've yet to work out whether the grievance system has much effect - I've incurred high grievance for taking city states while still being able to ally with everyone, even the ones whose agendas I repeatedly violate.
It seems there may be an issue with the friendship/alliance system - you can get friendships almost immediately, which is fine, but once you have them you can apparently keep renewing them indefinitely whatever you do. There's no AI backstabbing in Civ VI so you're always completely safe from any civ you're allied with. Things that violate agendas or that the civ otherwise dislikes should much more strongly reduce their incentive to renew an alliance, or their odds of going from green to yellow.
This I suspect is why AIs end up fighting each other a lot but not the player - AIs will generally have militaries fairly comparable to one another, and it seems that AIs rarely or never declare friendships or alliances with other AIs. So while the player gets a lot of positive modifiers for doing so, the AI doesn't.
I think the devs should just improve the behavior attached to agenda related to warmongering so that we can expect more warfare from the likes of Chandy, Alex, Gorgo, Genghis etc.
AIs don't differ in their behaviour in any detectable way with virtually no exceptions (Gandhi and Poundmaker won't declare wars early where other civs mostly do, but that's the only difference). Some of those civs have agendas that make them more prone to dislike you if you're a good military target, particularly Chandragupta (but conversely if Chandragupta isn't immediately next to you he'll be the friendliest leader in the world), but Civ VI AIs do not have personalities in the way those in IV or V did - apparently they are coded with tendencies, but something in the modifier system or the general process of generating trait values for any given game prevents those from being expressed in any consistent way in Civ VI.