The discussions here sum up the phrase even Bad IT works too. How about a little common sense here. IT does not exist to support itself, it exist to support the business. The business is its customers. It doesn't matter what my preference is the only preferences that matter is doing what is right for the business.
As far as your support staff they are your best customer service reps. These individuals have the most contact with your customers. Processes are there for a reason, use them. Walk ups should be allowed only if your support tech is not working on another issue or calls are not waiting for him. Yes the customer at hand feels good but the person who called yesterday and followed the process does not. It has to be the right balance. I have seen people sit in support techs chairs waiting for them to return from vacation. Not an ideal process in my book. These same people are amazed when you ask them to log a ticket at how fast their support requests are handled.
This isn't magic but you need to build the right process and have the right knowledge in place. If you are going to make everyone log a ticket and allow no walk ups your support structure better have a quicker response rate than someone trapsing off to find a tech to tap on the shoulder.
Talk to your customers see what they want, use your own ideas of how you want to be served. Put yourself in your customers shoes.
My customers in my years of managing support staff have made comments that they feel like they get preferential treatment. There's no magic sauce just common sense.