A use for ticketing systems as your primary support method
In the past, I've been somewhat negative about having a ticketing system as the primary method of talking with the sysadmins. But I have to admit that sometimes such a ticketing system actually makes sense, and here's one example:
Suppose that your support group is sufficiently busy (you serve either a large organization or one with a lot of problems) that a single support alias would have too much traffic to be read by everyone all of the time. In this environment you have to hand support requests to a particular person, who then interacts directly with the user.
Now, consider what happens when a support request is handed back and forth between your people. Especially, how does the user know who to email with more information, a new sub-issue, or the like? As a user, you don't want to just email the last person you talked to, because you could be emailing someone who is now off-shift or the like and thus won't read your email (and add it to whatever internal issue tracker your support organization uses) for a while.
(In practice I suspect that people just send their email to more or less everyone who has ever sent them email about the issue, because you never know.)
An actual ticketing system that users use neatly solves this issue; regardless of who is involved with working on your issue, you always have just one place to put information. In a sense, it's abstracted away who exactly is currently handling your request.
The appeal of this likely depends on how large and busy your support group is. In a small organization where everyone can just be on the main support alias, there's no need for this at all (well, mostly). As the organization gets bigger and bigger, the attraction is going to grow, and at a certain point I suspect that a ticketing system becomes inevitable.