Kit, I read this as your T saying - albeit in a kind of kack-handed way - that she is human too (in having wants or needs that are not necessarily healthy, but that it's ok to have them). That in saying she loves to feel wanted/needed by her clients, she was trying to normalise your feelings of wanting her, and that being wanted by her clients makes her feel good. So you get something (a T you like and trust) and she gets something (job satisfaction and feeling privileged that she is helping people).....maybe.
Just my take on it and I could be wrong. But that is what stood out for me in her text to you.

I really hope your home meeting with T and your parents goes well. Like others here I'd be a bit wary that she just sprang it on you without any discussion with you first. My ex-T did a similarly spur of the moment thing once, and said she was driving over near to where I live on the way to somewhere else and would come and park outside my house. That was so out of character and totally freaked me out, so I can't imagine being faced with the scenario of my T coming into my house uninvited. But you can set boundaries for any future contact she has with your parents, if there is something you aren't happy about, say so. It's your therapy after all.

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