I don't currently see it as overused. But I certainly see your point that we don't want to get rid of all questions which can fit this schema. My view is that something should be done about the "Why did" questions too, because:

1. Many of them share the same problem as the "why not" questions 
2. Some of the "why did" questions can indeed produce a very interesting answer. But if they do, it is an answer to another question. 

##The problem

The problem behind "why did feature F not evolve in organism O" is clear: evolution does not have motives. But the "no motives part" actually also covers the "why did F evolve in O". I trust that all our regular users know how it goes, but I'll repeat it - a feature can evolve because there is selective advantage in having it, or because there is no selective advantage against not having it. The second reason makes for lousy "why" questions. In the first reason, an answer saying "because there was selective advantage for it" is a boring answer. The interesting answer comes when we explain what role does F have in O, which as a side effect makes it so amazing that there is a selective advantage for it. 

*The "why did evolve" question is actually a layer of misdirection*. It allows a false assumption to take place ("If it has evolved, there must have been a selective advantage for it, so the two questions are equivalent"). 

##My suggestion

We can look through the uninteresting layer of "why did" and reveal the real question beneath it. **Reword "Why did F evolove in O" into "What role does F play in O?"** 

 - Sometimes, it will have a good answer, and it will be the same answer as to the "why did it evolve" formulation. Compare the answers to "why did an opposable thumb evolve in humans" and "what is the role of an opposable thumb in humans". 
 - Sometimes, the answer will be a simple "none". If this is so, the formulation (or the trouble finding it) may help the asker realize this. Compare "Why did the humans evolve an urethra going through the prostata" from [this question][1], to a possible rewording such as "What is the role of the piece of the urethra which goes through the prostata in humans". This sounds a bit weird, but there is no real way for a layman to know that there is none, so I guess people could ask it, so we can give a simple answer. 
 - Sometimes, the answer will be a "none", and really obvious. Imagine somebody who wonders "why do we have 5 fingers, and not 4 or 6". He'll be forced to write the question as "What is the role of the human fingers?". With some luck, he'll notice himself that all of the points would apply to 4 or 6 fingers, and won't bother us with "but why exactly 5?". If he asks it nevertheless, and we have to correct him, this might be the critical piece of information which makes him grasp how evolution works and how it doesn't. 

As a bonus, this will spare us from repeating every single time that evolution is not a human engineer and does not go around thinking up optimal solutions. We can still point to the canonical "why not" question when editing to reword, with the suggestion that the OP reads it in order to get background knowledge.  

[![enter image description here][2]][2]


  [1]: http://biology.stackexchange.com/questions/40503
  [2]: https://i.sstatic.net/VVt6p.png