jockbir,
While it is true that additional help is what everybody truly wants, documentation also has its place. Documentation can be used to accomplish several tasks at the same time.
1) By forcing users to put requests in writing, you're forcing them to think about the problem they're having. This can lead to them realizing they already know the answer, or at the very least save you some time figuring out what problem they're having.
2) Also by forcing users to put requests in writing, the ones that aren't important will go away because it actually requires some effort on their part.
3) Having requests in writing can help prioritize which tasks need to be accomplished first.
4) Retaining documentation about problems can help remind you which solution worked when a difficult problem crops up again.
5) Showing where your time goes can help justify to management why you are requesting additional help (which we all agree is probably a good thing).
6) Documenting where your time is spent can help when management dumps more work on you. "Yes, I can take on another project, but it will cause something else to slip. Here is what I have ahead of me. What do you think my priorities should be?" (Or something like that.)
7) If you need to go to higher levels for support (such as a manufacturer), documentation helps you convey what problems you're having, and reduces the chance that you'll forget to mention an important detail.
8) In the event of a conflict, documentation can be used to show what events happened when. If you have written documentation, and the other party is going off of memory, you'll often have more credibility.
Above all else, every situation is different. What works in one place may not in another. However, simply discarding documentation because you're spending the time trying to keep up with the ever-increasing workload is like (to quote a post-it pad I once saw) being "too busy mopping the floor to turn off the faucet."