The issue is not with problems, but with the arbitrary nature of this as a learning tool. Getting a page to fix an issue that you forsaw and prevented is dumb. Teach them to make resilient systems rather than get out of bed.

I have never gotten up at 3am to fix an outage because outages do not impact systems that widely. If it is a network problem, let the network team do their job. All of your other problems are solved with multiple HA/ load balanced servers, monitoring, and proper testing.