Hi, let me try to explain a different way
John@customer1.com sends email to support@company.com. Ticket is created and the user is John. John gets a notification that a ticket has been created - Perfect
Jack@customer2.com sends email to ron@company.com. Ron gets email in his normal email system. Ron forwards email to support@company.com so keeping attachments etc. Ticket is created and the user is Ron. Ron is an agent so logs into the ticket and changes the user to be Jack. So the ticket use is now jack but he does not know. because he does not get the ticket creation email
So, Yes, this:
"We have people email IT individually all the time. I open the support@company.com mail box in Outlook and drag and drop the emails into the inbox, and it opens them as the person that sent the email."
would work fine if it was just me
But that would mean all of our "named" staff would need to have support@company.com set up on their outlook systems (and some use gmail rather than Outlook). Which would also mean they would receive all the normal support@company emails in their outlook. (Guess you use piping so you don't get all the emails in your Outlook. We could not get that to work.
Our support staff are really support for pipe support systems, not IT support. So their IT skills are not great which is one of the reasons I wanted to switch to a ticketing system