Are you insane?
"Accept all forms of help desk requests (ticket, email, phone call, on the floor), keep the requester in the loop, be pleasant and respectful, and you will make the user satisfied with the service"
Yes, be respectful, be pleasant, keep the requester up to date. But a formal ticketing process is key to support success. Most importantly if your helpdesk is undermanned (as it is in most companies I've worked for).
Small companies that have maybe 20 or 40 employees, maybe the approach of "anything goes" works, but not when you're dealing with a larger more global company.
For example, what if the support tech is away for a week and they're getting requests for support? If it was in a ticket system, someone else could pick it up. Or what if the technician was working on something just prior to taking their leave? With a ticket system any other tech can view the entire history and get the job done.
The other problem of course is when you try to justify a new tech. It's far easier to show the work being done by reference of tickets than comb through everyone's email, wracking everyone's brains for drive-by support, etc. Tickets show exactly what is being done by the helpdesk, how rapidly support is rendered, who is a common requester, etc.
Last, but not least; a good ticketing system that's properly used by the helpdesk staff also provides a knowledge base for users and for the helpdesk tech who takes the call. Problem loading program ABC with error XYZ? Ah, ok we had that problem last week, solve it by doing DEF.