Sasuke would never have learn Chidori

That's if Kakashi didn't teach Obito Chidori.

Why would Kakashi teach Obito his signature technique

While we don't see teammates sharing techniques except Boruto and Mitsuki with Purple Lightning, it's not beyond the realm of possibility, if Obito stayed in the village.

Naruto didn’t teach Sakura rasengan just like she never taught him her chakra enhanced strength technique. So I don’t see why Kakashi would want to give away his prized Jutsu especially in this timeline where Obito survived and hadn’t bestowed him the sharingan.

We don't see in the Naruto series, but Kakashi could teach it to Obito since he's the one with the Sharingan. Unless we're using Kishimoto's idea of individualizing team members' jutsu for the story.

The problem here is that he doesn’t have the incentive to do that. Without the boulder incident, I doubt Kakashi would consider Obito as a close friend, much less someone he would share his original move with.

That makes sense. There's also the timeline of Obito returning to Konoha after Madara saved him instead of going rogue, which Obito saw imaginary visions of in the actual story. Kakashi and Obito are shown to be much closer in this imaginary world, thanks to the Battle of the Kannabi Bridge and Rin's death.

There, Kakashi would definitely have the incentive to teach Obito the Chidori, and maybe that could contribute to Obito getting recognized and then becoming Hokage.

Kakshi taught them it fits

I think the thousand years of death is a very important technique only kakashi could ever teach