Which is precisely why they are arbitrary; they arise from actual game scenarios. But I find it odd he should distinguish the number of pawns in rook endings (R+1, 2 or many P) v (R with or w/o P), and also missing are combinations of 2 minor pieces, e.g. 2B v 2N, B+N v 2N etc. I don't believe the minor piece endings are so rare... it's almost like he decided which material imbalances he wanted and searched only for those.
I have nothing against this study, in case that wasn't clear. In fact, it's a great source of information and direction in endgame studies. Just a few queries I have about it.
The categories are arbitrary, but I don't fault him for that. What would be really informative was some info on how he pruned the data to eliminate the simple issues, but I don't see that happening short of asking GM Mueller himself. The little extract from FCE seems a very simplified version of the method.
Which categories are arbitrary? The categories represent percentages of endings that occured in a DB of 1.7 million games.