You're proposing an incredibly overpowered concept that would just get the champion nerfed into the ground, again, like he did back in season 4.
Kha'zix does just the same in teamfights as any other assassin, in fact maybe better due to the resets on E.
I use his ultimate for a lot of varied things, but it's most effective to skirt around uncontested in team fights to jump on the appropriate carries.
I also play a lot of Kha'zix, and I can tell you that resetting his passive nets me a minimum of 3 kills a game that I wouldn't get otherwise.
The only real changes I'd like to him are numbers changes, and maybe a rework on his ultimate that gave it a proper charge system that reset one charge on kill, similar to Akali's ultimate. There's often times where I only end up using one of the two charges as the first stealth was enough to do what I needed.
What I can tell you will help is when Assassin's dagger actually comes out as an item, it'll return the game to the assassin meta almost instantaneously I'm just trying to figure out where it should go in my build for Kha'zix.
Also, I looked up your Kha'zix games, and if you like the way you build awesome, but try this build
then boots of your choice. I find it works even better than the build you're using, which is the one I used to use. 40% CDR, 30 Flat armor penetration, armor shred with cleaver, I nearly do true damage between the items and my runes, when jumping on carries. I simply don't like the Tiamat build as it's not nearly as good unless you can instantly buy ravenous hydra, as there's no more cleave passively on Tiamat.
Above all else, I think the thing that would fix Kha'zix's spot in the game more than anything else is if the old last whisper returned. Only penetrating bonus armor instead of all armor was a huge hit against Kha'zix as he's already not great against tanks, this just made it worse. Maybe they could play around with putting some sort of armor shred on his abilities, nothing crazy, but say you land his jump it shreds a % of the targets armor, maybe similar to Urgot's E so it scales with ranks in the ability, something like 10/15/20/25/30.