I play multiplayer campaign exclusively and do a lot of head-to-head. For the most part fighting Ikit Claw when he can bring Doomrockets to any engagement was difficult to say the least but at least it was pretty fun. The Under-Empire is also a really fun mechanic even when you are fighting against it but it was one of the hardest parts to fight against and on it's own set me back a lot. I'm not saying though that the Under-Empire is a bad mechanic, I actually in fact think it's fantastic and extremely thematic but the way that the Under-Empire can spread randomly doesn't lend itself well in head-to-head campaign mode.
So to clarify on this, to counter the Under-Empire as a result of the random spread I had to spend a ridiculous amount of time and money building detection in a half dozen regions. This means that I ended up using tons of building slots and tons of gold building those structures to stop a mechanic I can't even do anything about outside my own territory short of declaring war on anyone I even suspect might have an under-city beneath them.
But that's not all.
Because I have to devote heroes singularly to the goal of disrupting Skaven Warlocks and detecting under-cities I have to use and upgrade even more building slots to accommodate the higher hero cap I needed which had to be supplemented further again because the Skaven kept sending assassins to kill my heroes and of course the heroes cost a fortune too which meant my economy went down the toilet even further which meant I had to devote even more buildings to my economy. Finishing it off it also adds rampant Skaven corruption which meant I had to build even more public order buildings than I ordinarily would have to.
So in order to counter this in a head-to-head I had to sacrifice easily a dozen building slots across four provinces just to keep up with it otherwise I was going to be insta-gibbed by a doomrocket - which did happen because despite everything I tried I couldn't detect the under-city beneath my provincial capital despite knowing full well it was there.
It's not all bad but since the under-empire can randomly spread it means that I have to constantly play minesweeper to try and find if a new Under-city spawned which is tedious, long and boring. I wish I didn't have to deal with that.
Another issue was the potency of early access Jezzails and Rattling Gunners in a tier 3 building from Skavenblight. I don't believe that either whether individually or together are so strong that they are in any way unfair but when your army's backbone is it's cavalry (I was playing as Carcassone) Jezzails become a huge problem. Ratling gunners were what really sealed it though because with my knights shutdown by Jezzails my only proper way to fight back was with trebuchets, archers and infantry. When I advanced on my mate's front line he always had a half dozen Rattlings gunners adjusted and ready to fire at whatever I sent. They cleaned up all my infantry in seconds and my archers did absolutely nothing against their armour. It was only after I reached tier 4 and gained access to Foot Squires and Pegasus Knights that I was able to begin to fight back which is fair I think given that Rattlings and Jezzails would ordinarily be tier 4 units as well.
So in the end the combination of these early access high tier units that hard countered my Bretonnians and the enormous amount of resources and time I had to invest in fighting off the Under-Empire mechanic made my campaign an absolutely one sided affair - this isn't even mentioning the Doomrockets my mate had seemingly unlimited access too. The only reason I was able to actually continue playing was because my mate (bless him) decided to stop attacking me because he too felt that it was a bit ridiculous and decided to let me tier up before continuing.
I don't think it's necessary to change how the under-empire currently works in single player though since it's very thematic, fun and interesting. In head-to-head however I'd appreciate if it C.A. would consider toning down these advantages somewhat to keep things fair but maybe not so far as to remove them outright since they are very fun.