Though the system is flawed because it is based on human standards to measure guilt they are not entirely illogical, and the ability to think logically about an issue, I believe, is something we have been given by God. And though mistakes happen - they don't happen in all the cases. There is also the issue of submitting to the governing authorities. Romans 13 from what I have understood deals with submitting not just to those governments who profess belief but also about earthly secular/pagan (render unto Caesar - Mark 12:17) governments, because though they are earthly they have been instituted by God and their ability to deal out justice is something also established by God. Servants of God whether they are aware of it or not?
Romans 13:1-5
Submission to Governing Authorities
13 Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. 2 Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. 3 For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. 4 For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. 5 Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience.