Surely you can see child molesters, alcoholics, and rapists as evidence of mankind being broken...
I actually see that as evidence of God being broken. If God created mankind then he should be the one to take the heat for making a defective product.
No, see that god only gets positive reviews. If a group of skilled surgeons and nurses work together, over many hours, to save someone's life, then God healed them.
If a man rolls his car while hitting the Interstate at 90 MPH, and he survives, then God's grace saved him.
The child that's starving to death due to famine and disease? God had nothing to do with that. Though according to the Bible, God caused all manner of plague on those he didn't like, and that included people who simply did not worship or know of him.
The hundreds of thousands of people who died in a Tsunami? God had nothing to do with any of that. Except according to the Bible, where God apparently caused all manner of disaster against those who didn't worship or know him.
Today though? Totally different god, apparently. Now God's a nice guy, wants to help you. All that stuff that happened? That's in the past, or you just don't understand how God moves in mysterious ways. God is wholly just, and good, and wise, and kind, and just wants to love you. He loves you! All that talk about war, and death, and famine, and disease, and the blood, and the slaying, and the drowning, that was just his message! His message of love!
Now, human beings try to save the starving child, and rush aid to the victims of that natural disaster? Yeah, it's mankind who is broken. It's mankind who is evil, not God. Just wait until billions of people die in the tribulation, as blood flows, natural disasters are wrought against the world, and each person suffers because they aren't following God. He'll show you how much he loves you! He only does it because he loves you!
Honestly, kids, modern Christian eschatology reads a lot like the symptoms of Stockholm Syndrome.
In short, to stay on topic, the humans in Star Trek don't need a savior, since they're doing just fine treating each other with compassion and kindness, eliminating disease and famine, working to make a better world for all humankind, and we, here in this universe, don't need a savior that likes to come in at the last minute, when other human beings have done all the work, only for him to claim the credit.
Prince of Peace, my ass.