When regular F-22s were already used to shoot down Chinese spy balloons they employed AIM-9 missiles, which are cheaper than AIM-120. But there's no need to get particularly close: in fact for safety they want to remain well separated from the target and never get on a collision course.
But in general all of your comments here have been deeply uninformed about how this stuff actually works.
I appreciate the heads up.
This is a low stakes brainstorming conversation, I presented my ideas as hypotheticals and shared my sources.
Honestly, I was hoping someone more knowledgeable would share any better insight on what the recently work on the SR-71 frame would be used for in practice. That hasn't happened so far, but that's fine.
"Your guess is bad because using the SR-71 for _____ in missions such as ______ would make more sense" would be stellar brainstorming about this beloved fan favorite.