What is the reason for the lack of Kayle junglers?

Solution 1:

Honestly, I think it's a bit of everything that hinders her as a jungler.

First off, her CC isn't exactly that great. A slow isn't bad, but a lot of the characters played at top level have gap openers or escape mechanisms. Tristana is going to rocket jump away, Caitlyn has 90 caliber net, Ezreal has arcane shift, Elise has rappel, and so on. Compare this to other junglers... Nautilus has his hook, Zac has a stun, Fiddlesticks has his fear, all of which are simply more reliable. This doesn't mean you can't get ganks, but it does make it more difficult.

Secondly, Kayle can fall behind irreparably. Her Q and W each cost a lot of mana, and if her blue buff gets stolen, she's in serious trouble. Sure, you still have some utility with your ultimate and heal, but Kayle's not a champion that has an easy time catching up when behind in levels/gold. This is particularly bad for a jungler, simply because they take more risks and get less farm than a champion in lane.

Third, her ultimate is only particularly good for one person tower diving. If they can outlast it, or simply run past their tower, it's not going to particularly help when ganking a lane.

In short, compared to the top level junglers, Kayle is a champion with sub-par gap closers, CC, and a non-damaging ultimate, and if she falls behind, will end up being utility-only. That's not to say she can't work, but there's simply too many risks and not enough benefit to bring her out in top level play.

Solution 2:

There are a few reasons:

• When junglers go into gank a lane, they need to be able to tank turrets if necessary, kayle can't do this well. Her ult as you mentioned is great for tower diving when you're the damage, but not when you're supposed to be holding turret aggro (it drops aggro when invulnerable).
• Kayle also lacks the ability to engage quickly and keep targets in place that other junglers posess.
• As mentioned in a comment, ae damage is less valuable in the jungle since season 3.
• If kayle is denied blue it will be really difficult for her to clear other camps quickly and she will be useless most of the early game.
• Building tanky doesn't fit her kit as well as other junglers and this is a pretty important requirement of a jungler.

This is not to say she may not become viable again (ezreal saw some jungle action recently!), but the current meta doesn't have a good fit for her in the jungle.