I never had the feeling that the important people in my life didn't care enough about me or didn't show interest/concern (more the opposite), but definitely felt similar from my last therapist, pretty consistently. I think it's part of their job to show interest, concern, to relate to clients, and I do believe that for some it is genuine caring, that they are truly interested in their work... maybe not in all clients equally, but in some definitely. And it's also part of their job to show concern even if their mind is somewhere else in the moment. IMO, therapists that fail to behave that way are probably rather self-absorbed and not very good Ts overall.