Americans can sail foreign, but most choose not to for various reasons. I, for one, am a little sketched out by having my pay check come from someone who may not be subject to US laws or regulations. Pay, working conditions, and schedule are other things to consider. A certain percentage of people who graduate from US maritime academies may also be in the US Navy/MARAD strategic sealift officer program and are required to sail on US flagged vessels for a certain amount of time (maintain US license for 8 years) after graduation.
I know a guy who graduated from Mass Maritime and sails for BW Group on one of their LNG ships, he does well for himself. A bit isolated, because he has been the only native English speaker on the vessel for quite sometime and most of the guys have a limited working knowledge of English.