We shipped a "personal" + "global/default" model for the home page and favorites menu earlier this year, and the model seems to be working pretty well at balancing the various concerns here and feedback seems reasonably positive. Anecdotally, the feature seems to be getting a fair amount of use (e.g., the open source installs have mostly made at least minor adjustments).
I think we briefly discussed extending the model to ApplicationSearch, too, although I can't dig it up offhand. I believe the rough gist of it was:
epriestley: If this works well, we should probably use it for ApplicationSearch too. [Then probably 3,600 more words.]
This got some previous discussion, but I believe there's no surviving task for it since I believe requests were largely proposing a different model which we didn't plan to pursue. One request was T9364, and I think this got some discussion in T4103 but we ended up pursing a smaller scope there.
An extreme version of this would be to tie it into separate profiles in T4103 so different sets of users could see different sets of globals, but I think that's probably more than we need to build and the case for per-group search defaults is weaker than the use case for per-group setting defaults. This is a real problem to some degree with the home page -- see T12871 and, particularly, T12308, for cases of administrators wanting to make different sets of items available to different sets of users with policy constraints.
See also PHI29.
(A cursory review of similar tasks doesn't immediately turn up anything which is directly adjacent here in a product or technical sense.)