I think a good client is one that does the hard work outside of the therapy hour. For me, one hour a week of talking is not enough to make progress.
My T rarely gives homework, but once she did encourage me to write about whatever I was thinking because for lots of people writing tends to just let it flow better than speaking. She said to try it for myself even if I don't want to share it with her. I now rely on this bigtime and I don't think I've had a session that I didn't provide the material for since it was first suggested. I hand my diary over to her at the start of each session and then she knows exactly where I am at.
I've written a couple of letters to people in my life, I've also described on paper exactly how certain situations can affect me. I also like to pretend to myself that I'm writing 'stories' , so I can distract myself from what I'm actually doing (describing moments in my life)
Anyway, my point is that T doesn't assign any of these as homework. I just do them anyway and T is always happy to work with whatever I've brought.
I'd strongly recommend writing down whatever comes to mind. Therapy is expensive enough for most people so it's worth taking the time in between to make sure you get something out of each session.