You're the one who raised the issue, so don't go getting all snippy if I point out a few details that don't quite mesh with the direction you prefer to go yourself. The choice for these US territories, in the early nineteen hundreds, was to remain a territory or to become a state. Nationhood was never really on the table. The borders of these respective territories were the same then as they are now, as states. Actual, limited warfare was fought over incursions into US territory, by Mexico. This is hardly a "useless sidebar."
You can quarrel all you want, but the central point I made remains. The United States has never had closed land borders. Our borders have not even been conrolled in the modern sense until the 2nd half of the 20th century. Stating this in no way argues in favor of the current state of affairs. However, it is important to the current debate to understand that we have no historical tradition of closed land borders, and that makes closing them now all the more difficult.