US citizens will keep traveling to Cuba posing as Canadians (they seldom admit being US citizens to the Cuban people)  on flights from Canada or Mexico. They have been doing so for years, and they have no problem since Canadian, Mexican and Cuban immigration officials just don't stamp their passports; those immigration officials are very understanding regarding the actual lack of travel freedoms in the US.

The way things are going in the "land of the free", I wouldn't be one bit surprised if Trump issues yet another Executive Order allowing Americans to travel to Cuba in groups but making it mandatory that every group has a Political Commissar so that the US Politburo can control every US traveler's movements while in Cuba.