American culture has grown increasing casual over the last several decades. But it is important to point out, that there are still places and events where people almost unanimously, dress up. So the issue is not that people refuse to ever dress up, the question is, why is church no longer on the list of places or events for which people dress up?
Recognizing God's sovereignty in his circumstance, Paul viewed himself primarily as a prisoner of the Lord, not as a prisoner of Rome. Thus, he must have reasoned that since he was incarcerated, it was because God wanted the people around him to hear the Gospel. He had the choice of either telling them his own bad news through complaining or telling them God's good news through evangelism.