I liked Kai's new looks in MK Armageddon. Not his outfit, that was ridiculous, but his overall build and model was pretty cool. I liked the dreads, want those to return, and of course his white tiger stripes. Not that hot on the beard though, looks kinda silly. If he's gonna have a bear, then it should be different.
He's an Afro-American turned Shaolin Monk, without turning all Wutang which would be the stereotypical way of doing it. His look in MK4 was rather simplistic, but he was given a unique vibe with the wider headband and the one-side vest.
There's indeed potential here, and I would love to see what NRS would do with him.
Story-wise... it's tough. Since Liu Kang never recruited him to be a Shaolin Monk, question is, would he be that in the new timeline? I can see, as you said, that he could be linked to Kenshi instead somehow, or maybe to Kung Jin. Or maybe he would be completely revamped, having a whole new storyline with a new fighting style. Alot of people seem to link him to Capoeira due to his spin kick, but then he'd just be seen as an Eddy Gordo rip-off.
I would like for him to be a more hard-hitting and acrobatic kung fu fighter. I can see him do alot of different kinds of spin kicks as his main moves, maybe inspired from Capoeira, but mixed with some kind of style of kung fu. Something very Jet Li-like.
So yeah, would love to see Kai return, along with many others of the 3D era. But let's see if NRS are willing to give them a chance.