That’s fine, but then the MP should hire an assistant to manage their email if it detracts from their deep work. Donald Knuth does not have a sworn duty to represent people; he could go and live in the woods for all it would matter
They had a sworn duty to represent people even before the computer was invented. He’s not failing that obligation by not answering email, tweeting his every though or ignoring Facebook friend requests. Your preferred path of communication isn’t the same as his, that doesn’t mean he’s failing to communicate.