2m / 70cm repeaters for disasters and emergencies?

This remark got me thinking.

Although most 2m and 70cm FM amateur radio repeaters in North America and Europe have a tiny utilization rate (per 24/7), I understand one justification for their existence is for emergency preparedness, e.g. to be used by the amateur radio emergency organisation in the relevant country.

I’ve read some repeaters are equipped with uninterruptible power supplies (UPS), including battery backups and solar-powered systems for emergency communication whilst many others are connected to the main power grid with very limited or no extended operating times after the power cut.

For national or regional emergencies, where power outages might last for days or weeks, I’m assuming only the most rugged UPS-based repeaters will remain operating over that longer time. Does anyone know if studies have been made in N/A or EU to show what the national coverage would be for the amateur network of repeaters? Would it be very patchy after a day or two?

In general then, what support realistically can amateur radio organisations like RAYNET-UK add to professional emergency services like the UK ones using the Airwave network (based on TETRA)?

Do amateur organisations like RAYNET-UK actually not rely on repeaters but use independent radios using battery and generator power, ensuring communication continuity when power grids fail?