I heard the oil story so I over oiled the crap out mine just to see, and even with a visible coat of oil on the MAF it worked fine. It was easy to clean off too.
On my cars I don't know if they add power or not because it's too hard to tell, and I'm certainly not going to dyno it, but how could they not? They certainly won't hurt power like paper can, especially as paper flow goes downhill over time. K&N isn't affected by dirt like paper is.
I can tell this about power; I run K&N on my Chevota and if you were slip a new top of the line paper one in there while I was asleep I'd know something was wrong very quickly. I know this because I've tried paper, twice, and it was a disaster. I tried whatever brand once, then I researched and got the best flowing one, but it didn't matter. I can also tell you that even with the front of the K&N packed with dirt I didn't notice any loss. I'm sure there was, but nothing even close to the very obvious loss of the best new paper element. Sure K&N doesn't filter as well, but after having wear a Covid mask for a year I'm sure you know how restriction feels, and I for one would rather ingest the virus than wear that frikkin mask ever again. So those of us wanting max power use K&N and accept you'll ingest a little dirt. Those that don't care about power should use paper. Simple.
Aside from power, I use them on my car because paper filters are very expensive and I would need to replace them often. I neither want to pay all that $ for a steady supply of expensive paper, nor do I want to open up both boxes all the time to do it. On top of that, every time I do take the boxes off I have to repair one of the cloth inlet ducts because somewhere along one or the other it'll come apart. I then have to re-glue it. I use Goop to do that fyi, which is basically extra thick silicone sealant. Perfect because it holds the fabric together without fail and flexes.
I've often wondered why K&N doesn't just make a more dense cotton filter to compete, filtration wise, with paper. I'd imagine it would greatly increase sales, and all those people wouldn't have to change, or even clean, their filters ever again. Fyi K&N does sell a prefilter for those that want to improve filtration. It won't really fit most cars very well, meaning you may not have the room since the foam is about 1/2" thick and in a sheet so you cut to fit your car. Part # 25-3918 or larger sheet 25-3930 if interested. I don't know how well it would work in some laboratory testing, but I can say when I have this on my Chevota it catches >95% of the dirt leaving my regular K&N basically clean.
Do not buy any brand of the thin mesh screen like the K&N PreCharger, which is a copy of Outerwears prefilters, either of which kill power more than a paper filter. People buy the crap out of them for offroad toys. All those poor people...
K&N now sells some much denser black foam which they say isn't supposed to be oiled, which just tells me it's too restrictive with oil. Probably too restrictive dry too, judging by looking at it. The problem is you have to use oil or it's basically pointless. But hey, maybe that stuff, if oiled, over a regular K&N has the filtration to match or beat paper, yet still out flow it?