I think I have my head around this but I'm hoping for some feedback.
The only time I can see the user's search scope taking effect is for things like message addressing and possibly replying to a message. Other than that, I don't see it taking effect.
More prevalent from what I understand is the initial search scope which is set by the call routing rules. These typically follow through to the next call handler if that call handler is set to inherit search scope. And so on, from the first call handler to the second.
Does the user's search scope carry forward when they "exit" the phone menu and either go the opening greeting or are transferred to another conversation?
Are there other times where the user's search scope is applied?
correct - the default is for * at the top level subscriber menu to take you to the opening greeting call handler but you can define the key using the custom key map utility and you can define the exit destination/action on a per user basis.
At the moment I don't think anything is on the roadmap for limiting admin scope - lots of work involved with that - but as ever such things should be requested via your account team to be sure it gets the proper weight during product planning (which is done well above my pay grade).
The User's search scope will "follow" them out of the subscriber conversation if the exit destination for the user goes to a call handler set to inherit - this will dictate which objects (call handlers/interviewers etc...) they can dial from the greeting of that call handler.
If the handler they go to has a scope set then it overrides and "tags" the call with that search space - much like language settings will "tag" and follow a call once set.
Search spaces only get used in the phone ocnversation currently (i.e. there is no admin restrictions on what objects you can see in the SA for instance - I get this question from time to time).