To avoid replay attacks one needs to sign a string that is tied to a specific message or time period
I agree. Even time period and message content aren't good enough: Let's say that the outgoing SMTP mailer at example.com is trusted. Spammer gets an account at example.com, sends themselves one message, then immediately copies the signature into forged headers for their spam that is sent out through whatever open relays or compromised machines they are using. The only way that the mail can be trusted is if it is being received directly from the example.com SMTP server. If there is any relaying, there is nothing that remains true and constant to sign.
But that is the situation we have today: My ISP's server can choose to refuse to accept connections from servers that are on a blacklist of open relays and spammers, and can, in theory, have a list of known good servers who authenticate their clients. If all the new header does is verify the sending mail server, that is done just as well by verifying the ip address at the time of connection.
-- sidney
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