For the Lord's sake. So when a believer submits himself to it, he is obeying the Lord. God's kingdom doesn't benefit from disobedience. We are to acknowledge God's control in all situations, not be troublemakers or lawbreakers. Judah was not to rebel against its captors, but accept its situation as part of God's sovereign plan.
Democratic theory is no less unscriptural than divine right monarchy.
Furthermore, civil government is an instrument, not an end. Men are proximate ends, but only God is ultimate end. The state owns neither its citizens nor their properties, minds, bodies, or children. God is the ultimate authority who calls us to obey His divine law. Although Christ lived under the pagan Roman government, He didn't attack its rulers.