Why does God allow original sin to be passed on to children even though the children don't choose it?
God gave mankind free will, and, as a result, the sins of fathers (and parents in general) can be visited up on their children. This first occurred because of Adam and Eve’s original sin, which brought death upon their ancestors, as well as the contraction of original sin and concupiscence (see CCC 402ff.). So we see early on in human history that we can be negatively impacted by sin even though we don’t personally choose it.
Similarly, when Pharaoh refused to let God’s people go (see Ex. 9:1ff.), despite his kingdom suffering a series of plagues, he brought God’s judgment upon his people. Because of original sin, those firstborn were destined to die. It just came earlier than they anticipated.
Finally, we need to remember that sin doesn’t have the last word with God. He doesn’t abandon us in our contracted original sin and personally committed sins. He sent his eternal Son to redeem and save (see John 3:16-17). Indeed, God wants to save us all (John 3:16-17, 1 Tim. 2:4, 2 Pet. 3:9). Whether we are saved depends on our response to his offered gift of salvation.