From where I sit, it appears that the fly/batch sparge question is really centers around personal preference. There may be some (minor) differences in efficiencies and time requirements, but 1) I'm retired, so I'm pretty much immune to time-based arguments, and 2) this is my hobby, so some inefficiency is perfectly acceptable so long as my enjoyment level stays high. I'm sure I'd feel differently if I ran a commercial brewhouse. Or if there was some evidence that one technique produced measurably better beer. But I don't, and there isn't (that I've seen).
There is one point that does seem to differentiate the techniques, though: the equipment requirements. I do a batch sparge in a version of a Denny-cooler in my kitchen, using two 5 gallon HLT/BKs. My kettles don't have any valves, and I don't use a pump. I usually heat pre-measured water for my mash in one kettle and sparge water in the second (I actually have a smaller third kettle for top-off or additional sparge, if needed). If I were to go to fly sparging, I'd need a pump, some valves, hoses and a sparge arm, or some sort of Rube Goldberg kludge. Not a huge deal, but i would take some degree of cost and effort to switch, and I'm not likely to do so without the potential of a better result.
Nothing against fly sparging; just nothing pushing me toward it.