The Monroe Doctrine was about preventing colonial powers from enacting NEW efforts to reach into the Americas, not about getting rid of previous control.
"The occasion has been judged proper for asserting, as a principle in which the rights and interests of the United States are involved, that the American continents, by the free and independent condition which they have assumed and maintain, are henceforth not to be considered as subjects FOR FUTURE COLONIZATION by any European powers." (emphasis mine)
Yeah, you can visit the EU by… sailing a ways Northeast(ish) from Maine, until you’re just south of (a part of) Canada. And by going to the Caribbean. And South America.
