I do tend to feel more satisfied when I stay on track and dive more deeply into it, yes. Same in my everyday life, I like to be focused when I am tackling problems and projects, and getting into all sorts of distractions tends to be one of my dominant avoidance strategies and sign of stress. I am not saying at all that this should be true for everyone, I think it's best to try and figure out why you feel unsatisfied.

Yes, I usually have less desire to email after sessions that I feel satisfying, but it's not a guarantee that it remains that way during the entire week... a lot of it is related to my mood fluctuations and obsessive tendencies that come and go. I'm no longer in regular therapy, just see Ts occasionally, and I find it's actually more effective this way because I go when I have something specific to address and stick with the topic, then I follow up myself in everyday life. Still have the urge to email the Ts every now and then but nothing even close to when I was going weekly. When I go regularly, I feel that it takes up way too much of my thoughts and mental energy and often becomes depleting rather than enriching. I got easily trapped in obsessive/addictive cycles that I know I am prone to by default, so this manifesting in therapy was really predictable for me.