A couple of shoulder-fire rocket launchers and some kalashnikovs wouldn't be hard to stash though, would they?
Presumably US flagged vessels are armed?
As a general rule, merchant marine vessels sailing under any flag are not armed. The US isn't "special" here.
Naturally, US military vessels, including the Coast Guard, are armed.
What of the right to bear arms then?
This is not a governmental restriction, but rather a commercial one.
Nothing prevents a shipping company from saying "In order to take a job on my private ship, you are barred from bringing weapons on-board."
Nothing prevents a country from saying "If your merchant vessel desires access to our ports, it shall not be armed."
The combination of those two (effects, not necessarily codified policies or laws) means that merchant vessels aren't armed.
We wouldn't let a <pick a foreign country not too friendly with us> warship steam into Boston Harbor. Same country's oil tanker or cargo ship? Come on in.