This is a decision that often needs to be made by middle management. For managers the most natural way to make this call is by evaluating the return on investment. To calculate the ROI, you need to compare the gain of an investment relative to the amount of investment. And this is exactly where things get hard, if not impossible. Measuring developer productivity is one of the unsolvable problems in our industry.
If a developer wants something which he feels will improve his productivity, not a lot of questions should be asked. The investment is probably ridiculously little, compared to the risk of depressing one of your codemonkeys. Developer happinness is at least as important as developer productivity. Happy developers tend to get passionate about their profession, and therefor ship better software as a result. And that's what we are all after, right?
I also find that peers saying something along the lines of "What's wrong with notepad?" are foolish. If you are most productive and happy using notepad, that's perfectly fine, but don't go belittling people who enjoy using more rich and intelligent editors. Your ePenis is probably large enough as it is.