Hello,
I would like mail to my primary address to be deleted after it is forwarded. Is it possible to set up a forwarder that does not deliver the e-mail to a mailbox on MX Route at all?
I actually do exactly this. Email to one account is redirected to another. I found it to work best to add a user filter (either cPanel mail filters, or if on newer server, Sieve filters in RoundCube). Make this filter redirect all email to another email address (account on the same server).
It also should work if you add the forwarder as usual (as a forwarder in cPanel/DirectAdmin) and then add a filter for that user to delete all mail.
BUT in this scenario you might loose bounces. Specifically when I sent an email to user+something@DomainA (which is forwarded to user@DomainB) that was rejected (as spam, I tested filters). But then the bounce (Mail Delivery Error) never came back to the sender, it somehow bounced to user@DomainB, and there it was deleted, due to my filter (delete all mail).
Conclusion: Redirect in filter, not by forward. 
This can also be done by just creating a forwarder and not an email account. If only the forwarded exists, there’s no mailbox for the email to be stored in prior to the redirection.
I like this approach. Seems to work with CrossBox filters too. I’ve settled on forwarding a copy of a message, and then moving it to the Trash folder. That way it’s accessible if I absolutely need to find it.
Is there a way to auto delete the trash at a certain interval in any of the webmail frontends or DA? I’ve found Roundcube has delete on logging out But that’s the closest I’ve seen.
Yes, for me it was a case of repurposing, and I already had many plus aliases for that account (as in user+whatever@domain.tld) …