Kha's Q

says, no

How would you automate it? It's a spell, not an auto attack reset.

Would it work better if it was automated like Jax's W?

What do you mean by that? Like, automated in the sense it's an AA modifier?

Or automated in the sense it applies at the same time as Leap Strike, where Kha'Zix would apply it with Leap?

As Kha'Zix's Leap is an AoE skill - you'd kind of need to do add Yasou Steel Tempest+Sweeping Blade special combo for that to work out, and considering how powerful Kha'Zix already is, he doesn't need to be even easier to use properly with less time to react against him.

Wouldn't say so, especially since it has longer range than Kha's auto attacks. Making it an aa modifier would be an unnecessary nerf.