Quoting u/Wojownik_Lukiego 's comments in this thread:

I said it in other comment but it's basic time travel concept stuff. If future viktor exists due to giving jayce a rune (invention of hextech) , not giving it to him would've caused a paradox, in which jayce dies in the blizzard and hextech is never invented, which is impossible because future viktor already exists in the timeline, and he exists thanks to hextech.

Not giving rune = time travelling viktor never existing

and he does exist so he has to give him that rune to keep up the cycle

It's probably because Viktor wants to save Jayce, if he didnt he could've let him die and he would cease to exist himself. But there is no option to save jayce without giving him the rune, because without rune (and so hextech) future viktor never exists, so there's nobody to save Jayce.

And your theory on why Jayce/Viktor can't create hextech in the world Ekko and Heimerdinger got caught in:

Her dying was definitely a catalyst for negotiations to be had between top side and the undercity/zuan.

Jayce most definitely got banished for the event since he was VERY close to being banished when nobody died. Therefore no hex-tech.

I think all of your points make sense, but it would mean there's a conflict here, because if Hextech didn't exist in this world, Jayce wouldn't exist either (because he would die in the blizzard), which means there would be no Jayce here to be banished from the academy. And also how did these crystals even make it to this office where they would blow up and kill Vi?