A pitri is not simply a dead person. The dead are made into fathers by rites performed after the cremation, and until those rites are complete the deceased is in an unsettled condition that the tradition treats as dangerous to itself and to the living. The offerings of rice balls, made in a sequence over a defined period, assemble a body for the dead and then join it to the ancestors already there. What comes out of the process is a member of a class, and the class receives worship.
The obligation that keeps this going is put in the strongest terms the ritual literature has. A man is said to be born owing three debts, and one of them is to the fathers. It is discharged by having sons who will perform the rites in turn, which makes the ancestral cult a chain rather than an event: the reason to have a son is that somebody must feed the fathers, and the reason to feed the fathers is that one will oneself become one. That is a very tight piece of religious engineering and it has held for three thousand years.
The offerings are made to three generations, and the ancestor who passes beyond the third is understood to merge into the undifferentiated body of the fathers. An annual fortnight is given over to them in the Hindu year, when the rites are performed for the line as a whole. None of this is antiquarian. Water offered to the ancestors in the cupped hands, the annual fortnight, and the rites at a death are current practice in households that would not recognise a single other name in the Vedic pantheon.