I think a lot of people's perceptions about their T's get into descriptions; my T, whom I'd seen for 9 years before, on the first session I saw her again (for another 9 years) said, "I am not an ambulance chaser!" and I could have taken that to mean she didn't care but how some T's set their therapy boundaries and how a client might interpret that could have a lot to do with thinking a T did not care or go "above and beyond".
I had a T (who recommended my final T to me) who called me when I didn't show up to a group session, which I took to be unusual, but I always show up for everything, a little ahead of time and very faithfully and her calling me was obviously related to her and my relationship and perceptions of each other. My 20-year T probably wouldn't have; as a matter of fact, I was in the hospital ER for 14 hours one day when I had my appointment and called her at the last moment I could, when I knew I wasn't going to get out of the ER in time, and next session she told me she requires 24 hours notice for missed sessions and next time she would have to charge me. I didn't take that to mean she didn't care, I just gave her heck back for it being the first time in 6-8 years that I'd ever heard of that policy

It wouldn't have changed what I did; I would still have paid for the last minute cancel, if that was her policy, if only to help myself, keep being able to go to my normal session if I was able.
That is, to me, what therapy is all about; there are rules for my benefit as well as the therapist's and that's fine, the rest of life is pretty much like that too; I like knowing what to expect. It's hard enough to get to know the therapist and she, me, during the actual course of our therapy hours over the years without having to worry about the therapy "frame" and its rules and what to expect out of therapy hours. Therapists can't go "above and beyond" all the time, they're human, but if they do it once or twice, the client is going to "expect" or long for it all the time and I think that's where a lot of problems come in. I had a session, the same time every week, agreed upon by both me and the therapist and she and I always both showed up. We very rarely started late, and if it was the therapist's fault, we then ended that session late by however many minutes; I would hate having had a therapist with scheduling problems or who started late habitually or who I thought ended early, etc., especially if I thought it was due to other clients getting "above and beyond" sort of treatment.