EDIT: It's a long answer, I know. What can I say? I have free time on my hands.
First, I like resolving single-word-requests, they make my brain tick. It's good healthy cerebral exercise. The higher, more intellectually demanding questions I leave to the linguists and to the real enthusiasts.
Secondly, I believe they serve a purpose; many provide a rich source of information to visitors and they increase our vocabulary knowledge and understanding. Think of the number of times when we catch ourselves saying: "What's that word? It's on the tip of my tongue." I would like to think that any online research that asks: What's another word for [...]? Would lead that person to this site.
Having said that, there are moments when I think single-word-requests are the curse of EL&U. They can be so badly written. A poorly phrased question, lacking content and context, a visitor demanding (!) a single-word at all costs; only results making users feel cantankerous and irritated towards the OP.
Not all single-word-requests are of course straight forward, native speakers find it difficult themselves to write a clear, unambiguous description. Compare the first original copy of this question: Describing the type of family a person belongs to with it's final and 7th edited version
Now compare the first version above with this single-word-request A women's accessory...what's the word? The answer was obvious but only because the description was accurate and detailed. The OP's question couldn't be answered by looking in a dictionary, so she came to ELU and immediately got the answer she was looking for.
But I digress, above all single-word-requests are fun to participate in and really involve the whole community especially when the questions are; simple, grammatically correct and more importantly, open-ended. Look at this example Idiom for magic object (or idea) that fixes everything Yes, OK. It wasn't a single-word-request but the principle is the same and it drummed up a huge number of visits in two days. Personally, I had never heard of "a gold bullet" or "deus ex machina" before, and found the OP's question very useful.
To sum up, single-word-requests are like the typical crossword puzzles you used to find in newspapers; they can be taxing and extremely hard to resolve but the pleasure and satisfaction in finishing one is immensely rewarding, or they can be uninspiring, overly simplistic and bland. Hardly the stuff of vocabulary expansion. In writing this answer I was reminded of a comedy sketch entitled Crosswords by the British comedians; The Two Ronnies. (A comedy duo whose comedy routines I was not particularly fond of as a child but have recently rediscovered and now love.) I think we can all relate to the businessman's frustration (Ronnie Barker) with his fellow commuter traveller (Ronnie Corbett).