There is a technical solution to this - make Amber alerts specifically not bypass do-not-disturb. Others can stay as-is because I want to get woken up in case of natural disaster or other catastrophe.

My phone is always on vibration, but even on do-not-disturb, Amber alerts make it vibrate on my nightstand and that is enough to wake me up (especially since I have a work phone and a personal phone triggering at the same time).

Anyway, it's definitely a first-world problem but it is one with an easy, no-downside solution.