I know not all Christians believe this, but for those that do - why?
Why would God allow everyone else to be affected by Original sin, and hold us accountable for something we can do nothing about? And, why would God say that a baby who has done nothing but breath and cry be full of sin?
What is the purpose of original sin? Why did God create people to be full of sin?
It is not so much original sin so much as it is carnality. We are carnal - we tend to follow our own lusts and desires. When God created Adam (not only Christ was a son of God, Adam was briefly a son of God), Adam was perfect and deserved the title of Son of God. As a Son of God, one is naturally holy and above carnality. When Adam as a son of God decided to rebel against Him and engage the serpent, he officially lost his designation of son of God, and just became a lowly son of man. When Adam was a son of God, he was full of brightness and respected of all the animals of the field. We were supposed to be divine sparks from God that watched over the planet and everything in it. When Adam sinned, we became as animals, susceptible to carnality. Even more so than animals, because satan beguiled us with the curse of knowledge of good and evil.
Another sneaky satanic aspect to sin is that Adam and Eve didn't know sinning meant abdicating their holy dominion of earth to satan. When Adam and even sinned, they gave up the God-given dominion of earth, and now satan rules [the minds and spirit of most of] the earth. Therefore, since we are as animals now (a measly son of man as opposed to son of God), we are susceptible to the seduction of sin.
So, the purpose of the state of man serves several purposes. A few of I can think of off the top of my head are to show God's love for us as our Father (mainly through the sacrifice of Christ), to show us how ugly sin is so that we wont want to do it ever again, and to separate those that love Him from those that hate Him, or could care less about Him. God doesn't want another Lucifer in His family.
Babies are probably the most pure form of human. Babies (unless you are just an evil vessel from the beginning) are not accountable for their actions. In fact, there is such a thing called the Age of Accountability around Bah Mitzvah age, possibly a bit younger than teen age. Every single sin, even white lies, hurt someone somehow. At the base, it destroys you spiritually, as God is holy and cannot tolerate anything unholy in His presence. To me, God is good because there is nothing that says God has to do anything. Gods don't have to do anything, and do not owe their creation anything. When we sin, we rebel against the king of the whole universe.
If you rebelled against a Triad Gang Boss, or a Mob Boss, do you think they would send their only begotten (of man) son to die for your rebellion in your place? Some people consider the Triads godly in their own right, yet we rebel against the most High God and expect something positive.
God is naturally letting the result of our folly evolve, whilst especially protecting and watching over people that love Him. This protection does not mean perfect health, wealth, etc. It means no one or nothing can overcome you, not even death. God intervenes occasionally to show give signs, provide healing, or to alleviate His children pain. But this isn't owed to us, and frankly He expects us to handle a lot of things by ourselves, with the wisdom He gives us.