You are correct.
With our feet firmly set on the path to Empire (and disaster), we have two choices:
1) Open applications for statehood under the 1788 Constitution to the world.
2) Close the borders.
If we are to admit third world nations as States (not as bad an idea as it sounds at first, IMHO) we would first need to eradicate socialism here, so that we wouldn't have all the newcomers looting the US. This would require a change to the Constitution to repeal all socialist legislation passed since 1913 and to forbid future amendments permitting an expanded Congress from restoring them.
Maybe we'd better just close the borders.