The US Navy is bound to "adhere as closely as possible to" all laws governing ships of the US. The only blanket exception is mission completion. Colregs have exceptions that Naval Officers are trained in, for example sailing darkened ship with no navigation lights displayed. A Captain's first responsibility is to the mission, a Master's first responsibility is to the crew.
That alone makes the admiralty laws a poor fit for both. You cannot sue a Captain in the US Navy but you can down right fillet a Master. It's not so much that the Navy is exempt or allowed to slide on things legally, they have their own milestones of competency that more realistically reflect their own ships.
As far as might makes right, the entire reason our Armed Forces exist is to coerce our enemies to adhere to our biddings. The US Navy exists to remind our enemies that when our Army goes home and they go back to to their old ways we're coming back.
The US Navy may not be my first choice to share an ocean with but when I see choppers from the carriers landing food and medicine hours after natural disasters occur anywhere in the world at the same time they're conducting combat flight ops, supporting SEAL operations, monitering entire country's communications, evacuating Americans in peril overseas plus protecting the battle group and it is literally all in a day's work, I try to be even toned and give them a pass on things underway.
When Viktor Balinko defected with a MIG he asked to see a carrier underway. Flying back to the beach the next day he stated that a US carrier must be the most complicated integration of men and machine in the world. Be in awe of a US Carrier Battle Group. That goes for Russia too and they know it.