I like to tell people the first thing to go in a disaster is your phone. Communications get interrupted very quickly and easily. But I don't just mean phone lines. I mean the actual communicating and how it happens between people being a victim of circumstances.
What are those circumstances? Pure chaos. One of the things I learned while deployed in Afghanistan is the first report is always inaccurate.
During the wildfire on Maui last summer, no one knew who was in charge in Lahiana, not even the mayor. Wrong information was given to people evacuating. Police were blocking exit routes they mistakenly believed were closed due to down power lines. Those power lines posed no danger since the power company turned off power to them hours earlier. The 9-11 operators were not telling people to evacuate, or they were directing residents to the civic center that was cut off. In a town that was completely decimated, the mayor had no idea anyone died until the next morning.
The director of the Hawaii Emergency Management Agency (the local version of FEMA) said the National Guard was providing traffic control in Lahaina the night of the fire...after it was already destroyed and people were stranded in the water...which they went into to escape the flames. He had no idea about any fatalities until the next morning.
There is a lot to learn from the break downs. There are new procedures to put in place. Also realise that none of this is business as usual. The stress, the strict following of protocol. Not imagining something this bad can happen because it never has.
These are all human issues which you can't eradicate but you can help train for. Make it a policy for the power company to inform city hall and the first responders that they have changed the power status - doesn't matter why, it is good information to have and to make a regular practice. Instead of strict adherence to a plan, run the training enough that you enable a playbook, which allows for variances and taking in new information as it comes in.
While this is an example from emergency management, the principles are the same in a good business continuity plan (especially because EM falls under BC). Communicating and working with local agencies in partnership to solve an issue is actually a part of a business continuity plan. You want a playbook for agility. You want to have everyone operating from the same and accurate common operating picture.
When you see just how wrong things can go, you work to never make that mistake again. To the best of your human ability.