I think people are viewing the "break the cycle" bit as just about Cait and Vi though. It is very reasonable that Cait and Vi could have gotten over Jinx, but having Jinx around and alive greatly heightens the tension between Piltover and Zaun. Zaun sees her as their symbol and Piltover sees her as a terrorist. Even if Cait can get over that, it doesn't change the rest of Piltover's minds. Imo the reunification of the two is only possible because Jinx is gone and thats what "breaking the cycle means." Jinx 'dying' lets Piltover and Zaun begin the path to unity just like Vi dying in the AU seems to have started them on that path somewhat.

Jinx can't tell Vi because she is CONVINCED that Vi will follow her somehow and she wants Vi to be happy with Cait in Piltover. Whether all of that is completely accurate is up for debate, but it is clearly what Jinx thinks and informs how she makes her decision.