Thanks, as always, Cathal.
I definitely understand about the efficiency concerns - obviously, if it's slow, people won't use it. Still, I feel like there must be a way to achieve these varying goals. I'm mostly just thinking out loud here, but would it help if the user profile settings included an option for "Index for Search" or something that would tell the system to keep that (along with perhaps display name and email) in a special cache for rapid searching? Then, the "simple search" could just search that index? I don't know.
With that said, I think some of these suggestions could be done without too much trouble. For example, having a way to remove a third or fourth field from the advanced search seems like a simple design option. Also, since there is a way to filter by profile field already, why can't that be combined with a group filter? I suspect it means that it would always be running an advanced search, but that's often do-able, particularly on smaller sites.
As a minor other comment, it looks like there's no "loading" message for advanced searches - since they can take a second, that gets confusing.
Sorry to lump all of these together here, I just thought I'd see if anybody else had any thoughts on this stuff or if there were obvious problems I was missing rather than submitting them all.