Would you actually use or trust such an email service?
So the threat model isn't uniform. There's no one-size-fits-all. Depending on how you assess risk, you might reasonably conclude that government services pose less danger than private actors, and someone else might see the inverse.
Youre going to begrudge them an email account they host for ease of communicating with these same people?
Importantly, we need to be mindful of the lowest common denominator citizen who might have nothing but still be entitled to government services. Governments exist to service their constituents. The USPS is required to serve every US address (including mail delivery by mule into the Grand Canyon) [1], it is straightforward to provide ~1GB of email to everyone who needs it.
Here in Sweden we have something like this, but it's not one mailbox, but effectively one mailbox per government service. So there's one for medical stuff, and you get messages from the physicians who have looked into your problems, messages about booked appointments etc., and there's similar things for other government services that require multi-step communication.
In the abstract, email is actually a much better communication of last resort. A phone number requires you to maintain that phone number for the voice mailbox, or even be immediately reachable for more complex communication that can't be left in a voicemail. Whereas email just sits there until you can check it from many places, and the cost of maintaining an account is effectively ~zero.
And here we're talking about FEMA staff facilitating disaster victims. They could certainly have electronic devices to facilitate people checking their government mailboxes a lot easier than they could facilitate the same with phones. There could be terminals in post offices as well, for when the immediate disaster relief has gone away but someone still can't/won't have their own Internet access.
[0] fun fact: I tag senders using a wildcard character in the address, for example x-somebusiness@mydomain. When I give this style of email out over the phone, I invariably get responses of "you need a real email address", for which I have to explain my scheme and assure them that that is indeed my real email address (at least as far as they are concerned). To me this indicates that there is still a large contingent of people making up "email addresses" on the spot when asked, with no intention of ever receiving email - ie "Email address? Oh uh, John Smith At Google?"
(and yeah I know I could reduce the friction there by making the unique identifier into a nonce or other non-plaintext, and then keeping a mapping. alas, this hasn't really been a priority)
It's a lot like the difference between making a threat and posing a threat.
Obviously I'd rather none of these agencies have any of the data, but that ship sailed decades ago.