ForbidenMaster
Explorer
..the point being that in accordance with the rules dropping a shield (whether it is 'equipped or just held in your hands to carry it) is a free action. The rules make no distinction about being 'equipped' in this case, or in any!
If we take your definition of the rules, then you can drop armor as a free action. You are adding lines to the PHB that dont exist. A held item is held, and equipped item is equipped. The PHB says that you can drop a held item with a free action. It does not give rules for dropping an equipped item. When we are presented with a situation that is not covered in the rules it is up to the DM to decide what to do. It is that simple.
For what it is worth:
PHB page 213When you use a shield, you strap it to an arm and sometimes use the hand on that arm—your shield arm and shield hand.