Hurricane's specific purpose is to apply on-hit effects, so preventing it applying on-hit effects is not optimal. Also - Hurricane doesn't even apply the splash of Righteous Fury, mostly it just spreads Kayle's passive - which is far from the most exciting on-hit effect in the game.
Concerning Vayne - Silver Bolts specifically states in the tooltip that changing targets will re-set the bolt stacks, so you can only build up silver bolts to hit one target at a time. If Hurricane actually applied Silver Bolts on the side bolts, Vayne would be physically incapable of getting all 3 stacks on a target in any scinario Hurricane's side bolts would fire.
Also, Lucians ultimate is an ability that generally fallows abilitiy rules - (not critically striking is pretty much an ability rule - only 5 do). it doesn't apply on-hit effects. It would be broken if it applied on-hit effects. Dude doesn't need life steal and endless mallet procs on that. Pretty sure it used to in his Beta stage, but Riot realized that was a mistake.
As for Kayle - Hurricane isn't the problem with Kayle. Kayle is the problem with Kayle, which is why she got the nerf. Since before season 1 Kayle has always been a good pick - and she's generally gone through phases where she's amazing, Riot nerfs her, Kayle players get butthurt and move to a different champion, new players find a new way to break Kayle, Kayle is a dominant pick again, Riot nerfs her...
Kayle is an extremely strong champion though - her early game is very dominant due to the strengths of her AA steroids, her mid game has historically been really strong due to her burst and levels scaling, her end game has always been amazing due to her item scaling.
And on top of that her kit is extremely flexible - up until the %damage amplification was taken off of Reckoning she could be played as a top-laner, jungler, mid-lane, support, or marksman without performing badly enough to really call taking her any of those places trolling. Not even Lee Sin, Nidalee, Lulu, Jayce, or Elise is that flexible with their kits - and all of them have 7 skills instead of 4. Unlike all those champions Kayle also essentially fills all those lane positions and rolls with exactly the same AP/AS build, which means she's fully capable of having that range of flexibility regardless of what she builds - where someone like Nidalee with a lot of potential is wedged into one roll depending on her build.
And on the note of builds, Kayle can build any item in the game and make it work. Rageblade, Nashor's, Reaver, Thornmail, Hurricane - any item that's known to be bad is pretty much 100% garanteed to be a solid purchase on Kayle, the only time you really mess up is when you don't have a specific theme going for her build. Righteous Fury even applies spell-hit effects, so lots of fun is to be had with Torment and Rylie's.
I mean, Kayle isn't better than a solid chunk of champions at doing their roll - but the general balance rule of a Jack (or Jill) of all trades is they should be a master of none - and Kayle comes pretty close to being a master of a lot of them.
TLDR: Kayle was nerffed because she's Kayle. Hurricane wasn't nerffed because Kayle was being Kayle.
Silver Bolts with Hurricane, SotD with 
ult). Why did you choose to nerf Kayle the way you did over a fix like stopping Hurricane bolts from applying Kayle passive?
