That is an interesting proposal, @johseb.
I’d suggest a couple of tweaks to your suggestion. First, since Smart Groups can originate as saved searches from the Search panel, maybe instead of automatically prompting for variables, there could be a “Open in Search Panel” feature accessed by control-clicking a Smart Group, and which would immediately open a copy of the Search panel that’s populated with the parameters of that Smart Group. The adjusting of settings can occur then. I’m afraid I might be like other readers, and merely clicking a Smart Group and firing off a “change my variable settings” dialog would get old. It might be a bit too spring-loaded for usability. The advantage of using the Search Panel is that it combines parameters and results - and See Also, etc.
The other tweak is long overdue – the “Advanced” section of the Search panel needs to go away and those settings brought into the main sidebar of Search. If there was one unified sidebar then the kind of on-the-fly parameter adjustment that @johseb suggests (if I’m not putting words in someone’s mouth 
) would be easier to accomplish.
(I won’t get into the details, but my proposal can be adjusted to accommodate database scope - local or universal.)