Nice of you to completely ignore the main point while trying to steer the discussion into a useless sidebar. The stone cold fact is that our borders have been wide open throughout our history. To point out this fact does not equate with wanting out-of-control illegal immigration to contiue. However, we are a nation with no historical precedent for having closed, heavily fenced borders, so agitating for such is like spitting into the teeth of a hurricane. Can be done, but not without a lot of unpleasant blowback.
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."