I've had several T's. Most didn't take notes. Of the two who did - one noted things so rarely that when she did it was a distraction. I would wonder what it was about that particular thing that was noteworthy.
The current one takes quite a lot of notes, and will use them in two ways. She sometimes looks back during a session to quote back to me exactly what I said earlier, and she often brings in a chart of the image she is building of me. I like the precision, and I like knowing she has been working on me during the week.