I know that some ticketing systems do not have any form of protection against a fake "From: " field in email.

As you know, the SMTP protocol itself does not have anything against the end user putting bill@microsoft.com or any other email address in the From field. It's trivial to do this from bash.
And some support ticket systems blindly assign the ticket to the client with email address bill@microsoft.com and anyone can send a message with the following content:

Hello,

Please terminate all my services immediately! I confirm that I have a backup and all my files will be permanently lost.
Is there any support ticket system (that allows support tickets being opened via email) that performs some automatic checks in order to ensure protection?

They can do stuff like: check SFP, DKIM, check email if email is signed with a public key, send automatic reply and ask end-user to follow a link in order to confirm that he opened the ticket (less convenient).
What other suggestions to ensure email message authenticity would you suggest? Besides allowing tickets to be opened from web interface only or staff members that must ask an extra confirmation.

Or do you think that all this should be done by the mail server.