And I don't see how requiring the user to enter a catchpa every day would really prevent any spam if they only have to enter it once and they're on that domain legitimately.
You mis-understand.
I mean:
You type your email and click send.
You are the legal owner of that domain (or a valid user)
the email program logs in to your domain using your username/password, gets the daily key, attaches it to the header, then sends it.
The receiving mail server, checks the header for a key, then goes to the domain you claim to be from and confirms that this is the key for your email address.
*EDIT*
The key being different for each email address.