Hey! Good analogy! But now, let me play off of this just a little bit then.
You are right that He is more concerned with the inside of the cup, especially since religious types can have a habit of working hard to look clean on the outside while being filthy on the inside (spiritually). But now, I believe He ultimately wants both the outside and the inside of the cup to be clean. One verse for this might be 1 Thessalonians 5:23, "And may the very God of peace sanctify you wholly, and you whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ."
I think He gives commands because we are being prepared to become citizens of His eternal kingdom, and this will require obedience to the laws of the King. So to this end, I think the command was to become so purified that not only were our spirits and souls pure, but that the actions of our bodies eventually become sanctified as well in obedience to the Lord. I think the conviction of the Lord comes upon us not just to show us we are in need of a Savior, but to compel us unto ever increasing obedience, so as to be ever more pleasing to God.