Therapists should always take notes to cover their behinds if something goes terribly wrong! If there should happen to be a lawsuit, suicide, etc. those notes come in handy. Not to mention it helps them retain what you are saying to them and recall conversations from each session. There are so many clients usually and all it takes is a long day or sleepless night to accidentally confuse two clients or forget something really important that was said. I recall that being an issue for a couple people and it could feel hurtful when T forgets something that was discussed.
Taking notes also tracks progress. It's good to know my therapist could go back to day one and see how far I've come, what changed, what hasn't changed, what still needs work, etc.

There are so many reasons it is extremely important to take notes...