Good question. This is where trends actually become useful. During the height of the flooding, we had four topics trending on the top 10.. #yycflood, #abflood, Calgary, and Alberta.
I "manned" #yycflood and #abflood long into the night, passing along important information and answering any questions I saw anyone asking (eg "Is the tapwater safe to drink?" was a continually asked question, and monitored situation, all night). It was an absolute lifeline of information.
Calgary Police were incredibly responsive on it as well which was amazing to see. Somebody asks a question and everybody can see the answer. And our kickass Mayor Nenshi (who was a rockstar before, but is now a deity) was tweeting status updates from a helicopter. After he was awake for 43 hours straight, #nap4nenshi started trending. He complied. How's that for community feedback? :)
You're correct of course about it being primarily useful as a self-organizing tool, requiring a functioning internet to work, but I will dispute you on one point there; it's not (necessarily) the first thing to go down. Tons of people from areas with power outages were still using their cells to communicate. But then again, I suppose it depends on the particulars of your cell provider's infrastructure.