Nope, I do not say that children are unsaved, and neither does the RCC; we trust in God's Mercy. We also believe in what we call "baptism by desire", and/or "baptism by blood". It's not doctrinal, but, in short, it means that if the intention to baptise was there, either by the parents, or perhaps by the individual himself had he lived, then that infant would be saved.
As I said, it is selfish objectively speaking. Do you understand what that means? (I'm not trying to sound condescneding here, although I'm sure it's coming across that way). I did say exactly what you did, that to someonw who knows, then the behavior is selfish. Now, we go back to the topic at hand, which is original sin; do we, or do we not, have original sin affecting us? The answer is yes.
Now that then brings us to the discussion of baptism, it's effect and it's necessity.
Open Pandora's box...
Original sin as you call it, affects us IMO only by the fact that we all die a physical death. I am not held responsible for the transgression of any other person.
Baptism...The Bible clearly teaches that first one must hear the gospel of salvation, then they MUST Believe what they have heard, and then in Obedience of Faith they MUST be baptized. This clearly shows that one must be able to be taught and understand and have their own belief and obedience. I cannot make the decision for someone else....
I am going to anticipate a potential argument for baptizing infants...the passages that include the "households".....
Millions of people around the world live in households where there are no infants present. These passages are often used in a vain attempt to justify the unbiblical practice of infant baptism. But if one actually reads the passage carefully, one will see that this passage actually tells us no infants were present!
Acts 16:32-34
Then they spoke the word of the Lord to him and to all the others in his house. At that hour of the night the jailer took them and washed their wounds; then immediately he and all his family were baptized. The jailer brought them into his house and set a meal before them; he was filled with joy because he had come to believe in God--he and his whole family.
What this passage says regarding infant baptism:
1.) Paul and Silas spoke the Word of the Lord to all those in the jailer’s household.
2.) All members of the jailer’s family were baptized
3.) The whole family of the jailer came to BELIEVE in God.
Conclusion: Since every member of the jailer’s family came to BELIEVE (after having heard the Word preached to them) there could not possibly have been even a single infant present because infants cannot BELIEVE in God. Infants are not capable of understanding the “Word of the Lord”, nor can infants be described as “having come to believe in God.” Therefore, everyone in the household of the jailer was old enough that they could hear and understand the gospel being taught to them, and come to a personal faith in Christ. Only when an individual is old enough to believe the gospel do they become a valid candidate for baptism.