I agree, this is an excellent opportunity for learning. The most succinct explanation of obtaining a Pop Up IFR clearance I've heard is on Jason Miller's "The Finer Points" podcast from 6/18/2018, "Filing in Flight."
https://podcast.app/filing-in-flight-aviation-podcast-e34765539/ It's only 15 mins and tells you everything you need to know. The student in this example is far from perfect but manages to get an IFR clearance in the air while not stressing out ATC too much in the process.
