I would say so, yes. Or they might feel intrigued and excited by a client for other reasons, like if that client is, say, dedicated to doing the work and/or always have things to talk about. Or maybe they prefer the challenging sort who need to be drawn out and encouraged to talk. Or the client have an issue/condition that connects to them personally. Or they simply click with them.

I imagine it could also shift throughout the T's career. Maybe early on, they're excited by more difficult/complex cases. But then as years go by, they get sort of burnt out on them. Mine said early in his career, he'd be OK with a client, say, calling him in the middle of the night. But then he came to learn that he had to set more boundaries, how that works better for him. So he tries to avoid taking on the sort of cases where someone is regularly in crisis--I imagine he wouldn't want to work with someone with BPD, for example, or to do intense trauma work. (Though he's completely fine meeting with me multiple times a week.) I think that self-awareness is a good thing, to know their limits. Rather than trying to take on too much and getting burned out and not being able to serve any of their clients well.

But like KLL said, it could partly be about ego, or about "saving" or "rescuing" people, like a savior complex. And that would potentially be more problematic.