That would fuck with Kha'Zix mechanics and make it more beneficial to Q after auto/W'ing instead of in midair, which is not something that is good (reduces skill expression). Also, Kha's main damage is from his Q, so it's tough for him to get the execute to a good amount.
That being said, that's actually not a bad idea. New playstyle, much more revolved around his ult, but not a bad one. Instead of oneshotting with E+tiamat+Q in midair+passiveauto+R to finish/escape, he instead uses E+Tiamat+passiveauto+R+passiveauto (additional R+passiveauto if needed)+Q.
That being said, his Q would either need a much longer cooldown, something like 8 seconds, which would hurt his clear, or the damage would need to be nerfed so that he Q's once in the beginning for an ok amount (think a Zed E) then Q's again at the end for slightly more (think a Zed Q). That looks weak, but with 2 passiveautos, he has plenty of damage else where.
The only possible problem with this would be bruiser Kha, and a much longer CD on his Q would fix that (again, 8 seconds), which makes the first solution above better suited.