I'm personally against yet another thing which targets random irreplaceables, since current exo-waves and CPAs already do that. I wouldn't mind an AI force that hunts your champion (which should be avoidable, like the special forces), or the perpetual AI threatfleet champion.
Little to no warning attacks of opportunity belong to the threatfleet and hybrid hives; attacks like that which are directed against things which I can't replace are something that wouldn't be bad for the threatfleet and hybrid logic to consider when choosing attack targets, but I don't want the presence of a champion in the game to create an entirely extra force which hunts things which are at best incidental to the existence of the champion.
I also oppose attacks upon or the destruction of nebula facilities, unless some way is provided for the nebulae to contribute to their own defense. The one or two badly damaged space stations left in a nebula that never repair themselves, and the non-respawning nebula faction fleets that go off to patrol player worlds or sacrifice themselves in a once-off attack on an AI world, simply wouldn't do if there were a way for the AI to attack nebulae. In particular, the Dimensional Prison scenario, the Lord of the Colony Ships scenario, and the Ravenous Shadow scenario tend to leave badly damaged stations that would die to a stiff breeze, if the AI were able to hit them.
A unit that the champion requires support to defeat might be interesting, except that champions are supposed to be there for when the player doesn't have a fleet to play with (early game fleet build-ups, or later on in fleet rebuilds).
I could go with giving the AI a champion response squadron of some type (maybe an AI champion or two, or a small force of fleet ships and a starship or two, or something along those lines) which a well-managed champion could defeat but an auto-attacking champion couldn't defeat, and which could be avoided or lured away, since to me that seems more in line with champion play - you put the champion in the game because you wanted the players to have something to do while they don't have anything else to do, and for players who didn't want to have to worry about the empire management. Sort of like the Special Forces, except that it responds to champion presence rather than to human ships on an AI-important world. It might need to be given additional response criteria so that a player can lure the response squadron off somewhere else, though, or it becomes something along the lines of 'never lose the champion in a nebula you don't have a fully neutral or friendly path to', to prevent penalizing champion death during normal nebula play more than it already is.