I do not know what their criteria for acceptance are. My first, rejected, request discussed looking into distribution of available domains. My second, accepted, request was more carefully worded to indicate it was for general research.

The purpose of my request was for a personal research project to satisfy curiosity. My initial motivation was that there were things that seemed to be true about the distribution of available .com domains, and I wanted to see what the reality was. And, using NS queries would not scale.

I looked for the shortest English dictionary words available, percentage of various length domain names still available (alpha only and alphanumeric; with single numeral, two numeral digits, etc.), for non-words I looked at the distance from the closest English dictionary word, collected the patterns of common permutations of dictionary words into domain names, I monitored change rate, etc.

I've never "used" the information learned except to be able to speak with a little more authority in a single conversation where the subject matter came up. But, it was interesting to me :)