The issue is that unlike ADC's Kayle is mana dependent on being able to cs without getting poked, and even when she has mana she pushes the lane very hard, and is only ranged part of the time. Add onto this a couple more factors:
ADC's hit their power spikes before kayle, wave pushing bot lane without real escapes is very risky, Kayle does not have the steroids to hit the constant power of enemy ADC's, she requires time to stack up her passive/apply on hits/ready rageblade, supports are built to counter kayle through poke or hard cc during her ult, and since that is the role of a support when there is a kayle on the enemy team as a support it is easier to fight a kayle than play with one since supports will have more experience fighting them than with them, giving the enemy support a knowledge advantage and actually harming the ally support because in the end supports do more to control when and where the fighting happens bot lane than the adc's. ADC's bring power, but not much way to directly use it. Supports on the other hand offer the utility to control the battlefield.
So to conclude Kayle is generally inferior bot lane since:
-Mana dependent
-Only ranged part of the time
-Cannot burst as fast as ADC's
-Slower powerspikes
-Countered by supports
-Harms ally support more than the enemy one
Not saying that she isn't viable there, but picking her requires a support player with experience playing with her, and only into specific enemy team comps.
Oh, and add on to that that she is mostly AP, which harshly reduces the champ options of the other lanes since they basically have to grab 2 other AD champs and there isn't a large or very diverse selection of those for mid and jg.