Let's try this logic with the justice system in the US using your same argument.
That really stopped making sense all together, didn't it? What percentage of prisoners believe they had no choice, but had to commit their crimes -- and please remember, most didn't get busted for breaking just one law. Even if they did "just one crime," if you ever listen to a verdict being read, you'll notice they broke many laws. (It's rare when the verdict is only one "guilty," since the list of charges are judged one at a time.)
That's the American justice system. It doesn't call a person to some prison time for killing a cow. It doesn't require prison time for adulterous thoughts. It doesn't require prison time if you don't keep the Sabbath holy or have gods before the God. God's law does. And it's not merely prison time. It's permanent separation from God, death and hell.
So, really? When was the last time you "accidentally" put your desires above God's will? When was the last time you "accidentally" put your desires above loving others? What are the percentages on you "accidentally" sinning versus intentionally sinning? Are you innocent? Was your hand forced to do what you would never conceive to do on your own? Were you really innocent with the only reason to do what you did was because you were "born a sinner," or did you freely sin for your own selfish moments? You break God's law once and you deserve his punishment. Tell me you never freely did it anyway, and you may have a point. Tell me you're the only one who freely did that and you might have a point. Tell me those people in prison had no choice, and maybe you have something there.
Here's what God says on the subject:
John 3:16-21:
16 “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.17 For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him.18 Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God.19 And this is the judgment: the light has come into the world, and people loved the darkness rather than the light because their works were evil.20 For everyone who does wicked things hates the light and does not come to the light, lest his works should be exposed.21 But whoever does what is true comes to the light, so that it may be clearly seen that his works have been carried out in God.”
John 6:35-40
35 Jesus said to them, “I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst.36 But I said to you that you have seen me and yet do not believe.37 All that the Father gives me will come to me, and whoever comes to me I will never cast out.38 For I have come down from heaven, not to do my own will but the will of him who sent me.39 And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day.40 For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”
Romans... ah, nuts. The whole thing is a built-in case of how God works, so I can't give you the precise verse or chapter, but you really need to take it in as a whole.
Make no mistake. No one accidentally broke God's law. No one is sinless. Even if both my parents were murderers, it doesn't free me to murder. We deserve God's punishment. So it's mercy he chose some out of what we rightly deserve.