Interesting, but might be a hard sell to already email overloaded people now having to categorize outgoing mail. They might now even get an extra auto-reply mail for every mail they send.

There is also a emotional aspect in terms of everybody being told very explicitly that they are not important enough for an immediate reply.

In the worst case, a sender gets a message saying "that email you sent to Tom last week has been auto deleted. You can resubmit and maybe Tom will adress it later". It might be the honest truth, but I can't imagine a lot of people, especially customers or managers, would enjoy such a message.

As mentioned there is interesting elements, but ultimately it seems too engineer oriented and with a bad user experience for senders.