As a support main for 3 years now, I've experienced the same as well. First of all, playing Kayle in this "meta" is an "alright" pick. Neither good, or bad. Either way, what defines a "support" these days are quite an understatement. (Like... come on I've played everything from Poppy , Teemo and even (OMG I love) Anivia support which would be considered "troll picks"; at least I'm sitting at Plat doing the same as of now) Starting off, we can view her kit: Q, being able to harass and slow, W, being able to heal and provide a speed buff, E, poke/harass, and lastly R, "sustain ult". Since she is an "AP Mage", Spell thief would be the ideal start for harass + income. What makes Kayle such an "irrelevant" pick is her primary role of being a solo laner/jungler. Losing her damage build (carry) to a support (utility/tank) suffers, but thanks to the low CD's and utility from her kit she could "become" useful.
Pros:
-Annoying Late Game (Low CD Ults)
-Early harass/sustain -- If runes/masteries are built properly
-Can act as an individual "sub"carry
-Small CC from Q (up to 55% slow)
-Her passive allows her to shred enemy resistances
-2-3 seconds of immunity to damage
Cons:
-Very Squishy
-High mana cost (use wisely)
-No heavy CC (Cannot engage/disengage)
-Slow scaling champ (Doesn't peek well until late game)
-Utility kit allows her to have low CDs, but in return lack damage
-Long CD earlier in the game for R
Styles of support game play with Kayle depends on your ADC, Jungler and their Botlane as well as their Jungler; possible other factors could be roaming supports such as: Twisted Fate, Kassadin, etc.. The majority of the time you'll just be sitting there until 6, once in a while healing and/or harassing. The type of gameplay you want to play with support Kayle is a slow scaling game--which means you don't want to die a lot, you just want to (ideally) "afk farm". Although there are more "viable" champs like Morg, Janna, Annie etc. i'm not discouraging you from being a support Kayle main. If you're "good" at what you can play, I suggest you take it and develop it and make it something of your own uniqueness. It took me ~2 years to fully develop a specific rune page, mastery and skill orders to adapt to every situation for my Thresh. Hopefully it doesn't take you as long either. Sincerely, A Support Main :)
~And for all you "haters" out there, I would like to see you try climbing to Plat with supports only. :^]