Has anyone seen improvement in rankings when they removed domain privacy?
IMHO that's stretching things a bit far. All domains under my control, except for one, have had domain privacy enabled since day one and they all rank on the first page of results for their targets (except for one).
In fact the most recent one that I registered I felt needed to have registration details public because it's a host for many other websites -- in case someone needed to contact me concerning abuse issues (unlikely) or whatever.
The admin email I used for it is my webmaster email address for another account. Since it went public I am getting a very bad rash of SPAM in my mailbox and telemarketing calls on my phone. I have no doubt whatsoever it is due to contact details being scraped via whois. In fact the very first phone call came mere minutes after I registered it -- not an exaggeration. I knew it was due to public whois due to the nature of the call as well as who it was from.
I've also had at least one phone call from a scammer trying to represent themselves as someone from google. For years prior I haven't had to deal with any of this nonsense.