Allow me to put it this way: During WW2, the Soviet Union, despite not having the resources and equipment the allies did, still fought back the jerries with strategies, tactics and didn't leave their soldiers to charge the enemy without any good guns or ammo. Despite that, many people act as though all they did was throw as many men as they had at the enemy until the problem solved itself.
That is literally what Llavanya does. Pick a champion, send them to fight the dominas without any equipment, weapons, resources, etc. and hope for the best. The fact she doesn't even say a word to you until the PC, justifiably, decides to just say "fuck this shit" only tells me that for potentially most of her former champions, she just left them to their own devices without so much as bothering to check in on them to see how they're doing. Just leaving them all on their own to suffer God knows what kind of torments at the hands of the other dominas. Every lost you see in their realms is a testament to her lack of strategy, tactical thought or planning of any kind. We're also never told what she does at the start of the game when she's not around, so I can't even say something like "Well, maybe she's busy with more important things."
Then there's the part where she gets caught by Mary. Now, I won't put her torture at the hands of Mary 100% on her, but what I will say is that, for a domina, she was extremely stupid to just hang around in a spot where it was so easy for Mary to just grab her and fuck off back into her realm. Just think, if she was just a few more tiles away, she would've been perfectly fine and you would've never had to carry her around like a sack of potatoes after you rescue her from Mary's realm.
So in short, why can I not stand Llavanya? Simple, she's an idiot without any tactical, strategic or planning skills to speak of and she doesn't help her champions in any way unless they justifiably decide to ask themselves "Why tf would I do what she's telling me?"
