Just re-stating some things to be sure I understand:
I've read two primary concerns regarding public profiles;
(#1) Making a profile public makes the information contained in it available to the "public at large" (i.e.: any Internet user via a search engine).
My reaction: Yep. It's public. It doesn't matter by what means I access "public information" (whether via a search engine or via Geni.com).
(#2) I lose control over who can connect with or modify the information.
This I understand. This is a concern to be dealt with for any "community-built" system. In a lot of ways, the "Big Tree" of Geni.com is just a specialized Wiki -- and (especially in the early years, apparently) there were few means to control those who abused the 'collaborative' aspect.
Furthermore, there aren't currently sufficient "tools" for most users (even paying users!) to be able to collaborate solely with trusted family & friends -- if you will, having their own "sandbox", with "fences" between the "sandboxes". Right now, it is all just one big public playground where anyone willing to pay the admission price can go anywhere on the "playground".
In addition, there are insufficient tools (currently) to be able to "undo" mistakes -- by ourselves or by others. Most particularly to "undo" (roll-back) a merge once it is 'completed'. That is a major deficiency and source of frustration.
Does that reflect the main issues regarding "why to use private profiles"? (Oh, of course, obviously, for living people, private profiles should provide privacy for personal information.)
[ [I raised the question originally to try to clarify and separate the issues regarding public / private profiles from the issues regarding Geni.com policies which encourage -- or discourage -- collaboration and sharing. I know ... they *are* somewhat intertwined ...] ]