I have written plenty of things down for my T to read in session. I actually have a separate notebook where I write things down for/to her. Sometimes it's because I know I will have be uncomfortable saying something, and sometimes it's because the thing is complicated or delicate and I want the time and space to figure out exactly how to say it. My T has been receptive and agrees to read things to herself instead of reading them aloud or asking me to read them aloud (which I would hate).
I have found that it can be a useful way to share something. I think writing first does make it easier for me to share things in conversation with her too. But I think the main thing for me is that sometimes I feel like I can express things more thoughtfully and completely in writing, so that's mostly why I do it.