When a person dies, it is said after 12 days the soul takes rebirth in some other place. If the soul takes rebirth, then why do we hang the picture as ancestor and worship them?
If a person is reborn then why should one do shraadh? What you are saying is correct. In the ancient days, people were self-realized, so they used to know that so-and-so person has taken rebirth, and then they would stop doing shraadh.
Now you do not know, you are not a yogi, nor do you have the understanding to know whether the person is reborn or not. So, to take blessings, people continue doing this ritual.
It is said in Treta Yug and Dwapar Yug, people used to know that a certain person was reborn, and they would stop doing shraadh. The meaning of shraadh is to remember the person with complete faith.