Add me to the list of players that have never, ever, seen an AI be eliminated in any of my five full games. Sovereign difficulty. The idea that multiple AI would get defeated is bizarre. The worst I saw was one AI lose their third town to an IP. It was fantastic to watch them raze it to the ground as I moved in with my own settler.
Caveat: I play mostly on lower difficulties, and have not tried Diety yet, but my observations from about 20 games played through at least one Age and 3 games to completion at the end of Modern Age:
1. Yes, IPs can destroy AI Civs. In a game just this week I watched as Chang'an, the Antiquity Han Chinese capital, turned white after an IP took it, and shortly thereafter China and the city left the game. I could only see the edge of their 'empire' so I don't know what happened to the other Chinese city in the game - this may have been the result of another AI civ using its Suzed IP to take one Chinese city while the AI took the other.
2. I have seen numerous AI cities taken and razed by IPs, and even lost a couple of my own in my first games before I realized just how dangerous a Hostile IP can be in the early game. That means, against a suitably hapless AI (or Human!), there is no obstacle to the IP destroying the Civ.
3. All above applies to the Antiquity Age, I have only seen about 2 cities taken by IPs in (early) Exploration Age (and one of those was a first attempt at settling Distant Lands in a really, really Bad Spot). I have never seen IPs have any military significance or pose any threat in Modern Age.
And, to be clear, I think this is Not A Bad Thing. AI Civs do not generally pose any significant military threat early in the game, at least in any game I have played. That makes the IPs the only military threat, so making them a credible military threat to early cities just makes sense.
There are a number of things about the IPs I would like to see changed: more flexibility in interactions would be nice, like being able to leave the IP as a conquered Settlement instead of Always dispersing them through military action, more variety of military units spawned by the IPs (I have never seen them with anything but basic infantry and cavalry and Army Commanders on land: Unique IP units would be a nice addition), and even coalitions of IPs, perhaps as part of a Crisis Mechanic to provide a nee and deadlier military threat at the end of an Age. But right at the moment, I find their combat capabilities to be just about right as an early threat.