The wisdom behind rules of Islam is best known to Allah (SWT), His Prophet (SAWA) and The Infallible Imams (AS). We believe that all the rules from Allah (AS) are based on the absolute wisdom which aims to make our life real human life and guides us to the Right Path. We might be able to know some of the reasons but we can never argue for all the reasons.
Eldest son has the responsibly for the missed prayers and fasts of his parents because they served him before other children and he has the right to acquire special personal items (like rings, watch, personal Quran etc) from his deceased parents.
This rule does not mean that other children can not do that on behalf of their parents. In fact any of them can do whatever he or she wants to fulfill on behalf of their parents, but if it was not fulfilled, then the eldest son remains responsible to complete the remaining if any.