Getting back on topic, don’t we have the concept that great rabbonim suffered or were niftar as a kappara for klal yisroel?
A kapparah is not teshuva.
Think of it in terms of debt.
A kapparah is a note that wipes out a particular debt. Doing teshuva is resolving to not go into debt any further.
Teshuva is a *personal* process — the sinner confesses his sin, regrets his actions and resolves to no longer do so. Even if you could do the first for another person, there is no way you can do the latter two. They can only be done by the person themselves for themselves. No one else can make a resolution for you. No one else can regret something for you. Only you can do that.
The Wolf