Being a kappara for someone or all klal Yisroel isn’t the same thing as doing teshuva for the person. It’s more like nullifying curses or evil decrees.
Only the individual can do teshuva for oneself to be closer to Hashem, imho.
Even doing teshuva for the sins of our fathers or inherited from parents, on so on, are personal teshuva. We may redeem our fathers or parents, etc, but it’s not comparable to teshuva. It’s more like lifting transgressions. While teshuva is elevating them.
Yes we may elevate parent’s transgressions imparted on our souls, but is that really the same as doing someone else’s teshuva?