The idea is sound, I think. Treat emails, in a way, like we do phone numbers and house addresses. Except this doesn't ever change, when your name could (or you share a name with thousands of others). I wonder what the identifier would be for the address? Obviously SSN[at]usa.gov is a bad idea 😅
However, could you imagine the nightmare (on both sides) of a tech support call center for official government email account support?
I agree with you. I just think about how some government entities are less-than-efficient when it comes to the customer service thing, and that would probably apply here as well.
Probably also makes a difference if it's at the state or federal level. Local DMVs in some areas are, well, many jokes exist.