The third amendment was Boston's traumatic response to the British occupational forces that landed there forcing the locals to house and feed them.

It'd be like if the Carolinas came to the convention with an amendment drafted specifically about not being allowed to use terror tactics against enemy combatants because of Tarleton or if New York put in especially harsh punishments for treason because of Benedict Arnold.

Something that was forgotten since though is that this was a time before the development of professionalized civilian policing. Those soldiers were there as a policing force, and the third amendment was basically written with the intent that a police force cannot force the city they are policing to provide for them since policing is by definition not a service to the people who encounter it, but rather a service done to the people around the person encountering it.

Tl;Dr, Hamilton says Fuck the Police