somewhere in the world, a puppy gets ran over by a car, and another person decides to main teemo
Though I doubt the consequences you have claimed here, there are actually a few good reasons to max Q on Kayle;
1 - You're jungling
2 - You're laning against a champion that doesn't inhibit your ability to auto-attack them. One of the primary benefits of maxing E on Kayle in lane is that E's mana cost doesn't increase with rank, whereas Qs does. This can be especially important when you haven't dedicated any mastery points to the mana regen in the Utility tree. Interestingly enough, Teemo is a champion that you will want to max Q against, or better yet, not play Kayle against.
Every time you max E first on kayle
1 - You're jungling
2 - You're laning against a champion that doesn't inhibit your ability to auto-attack them. One of the primary benefits of maxing E on Kayle in lane is that E's mana cost doesn't increase with rank, whereas Qs does. This can be especially important when you haven't dedicated any mastery points to the mana regen in the Utility tree. Interestingly enough, Teemo is a champion that you will want to max Q against, or better yet, not play Kayle against.