They're usually pretty courteous in their interaction, which makes it all the more difficult to be "rude", in my case, by adding an exponential falloff in response times - after I realize what's happening, I tend to take a little longer for each reply so they figure out it's faster to just do the research on their own most times.
Agreed, and I do the same. They still get a courteous reply, but they also feel a little "pain" when they don't get a timely answer - an effective teacher.
Just giving them AI back is pointless. It means _your_ role is pointless.
My favorite phrase on that team was "What have you tried so far?"