We strive to make other settings persistent, but as you point out Exposure Compensation is not one of them. The design for this was based on the notion that lighting conditions typically change frequently for mobile users. I'll take your feedback to the team for consideration that being persistent would be useful for some users.
Thanks for the answer and for clearing that up for me.
Yes the option would be nice. I shoot my digital Leica all the time at a -0.7 to protect the highlights more and I've found this works perfectly for shooting on my iPhone in Lightroom. It would be great to have the option (at lease in the professional setting) hold its set value.