I can't argue, too much, with the use of water. Guess I've just gotten used to oil on diamond. I know most will probably say you don't need oil on diamond. Mineral oil is cheap. Anyway...I like the knife to slide along and I guess I've just developed a "feel". One advantage to oil...is that (depending on the metal of the knife) is I don't have to worry about residual water in the tang area, or under scales and flushing with WD 40. The vast majority of time, my knives only need a couple of swipes on a 600 or 1000 grit diamond stone, to bring an edge back...so it's quicker to not have to lube up an old traditional knife and worry about the water aspect.
But to the primary point of your question...probably the quick water wash, does get rid of the swarf faster.
One thing for sure...is, although principles are the same...like fingerprints...I think everyone develops their own unique methods. Just read the sharpening forum and you'll get a million ways to do it. I'll never argue with success!
Heretical Refurb / Mods of cheap old folders, since late 2018