Absolutely, yes. I think it varies from therapist to therapist but they all have preferences for the type of client they like to work with. My first T admitted that he enjoyed working with more complex clients because it challenged him and therefore he could set himself little goals to achieve along the way which made him feel good (looking back at that comment now, I should have realised that he had an ego the the size of the globe).
My third therapist said he wouldn’t ever work with anyone with BPD again due to it being too ‘draining’ as conventional once a week therapy was not enough to help.
I do think therapist egos can play a big part in these types of things if they aren’t self aware. They like an intriguing and colourful case as it makes them feel good for working with it.