Perhaps you're not filtering out requests on the basis of need, but on the ability of some individuals over others to figure out the unwritten rules and choose to play your game.
Yes, it is possible that people are gaming my tactic and I am optimizing for the wrong variable, but in practice that doesn't seem to happen.
1) thing is not essential, you saved the cost
2) a workaround that is inconvenient or costly exists, compare costs
3) you just caused an opportunity cost
In other words, you're breaking the process. Unless you're a process engineer and track both causes and results diligently you should not do that. Ever.
Obviously one should use common sense to avoid adverse outcomes. Inexpensive productivity tools get approved more quickly, whereas upgrades to perfectly fine but previous generation laptops may take a week or so :-).
Then the role of some person should be to gather such tacit knowledge and convert it into a usable and transmittable form.
Now if they do not know about one, they probably should be informed. :)
Some of them would call or email me with some really important, not previously discussed thing that they absolutely needed to have (but really didn't). Where in the past I'd immediately take this request seriously and discuss how many hours/days of work this would reasonably take, I now often give them an unusually high indication at first. If the conversation continues and it becomes clear that they really do want/need said feature, I'll come up with a more realistic indication.
http://dilbert.com/strip/1995-07-28
http://dilbert.com/strip/1995-07-29
The "approved list" as a philosophy or state of mind remains one of the best approaches.