The problem with this analogy is that while it's reasonable to think of oneself as the sole authority over one's own home, that concept does not scale in any meaningful way to the size of a country, unless the governing power is vested in a monarchy.

A great many political theses are advanced from all over the political spectrum in the format of 'You wouldn't tolerate X - so why does the government? We the people demand an end to X!' However, 'we the people', when taken as a whole, have a demonstrable tendency to disagree amongst ourselves, and almost never act in concert. There are all sorts of thing which we should find surprising or unacceptable within our own homes but whose existence we accept or at least tolerate within our county, state, or country because either a majority of our neighbors hold views which differ from ours or because constitutional or legislative power takes precedence over our own preferences.

A better analogy might be to consider the country as something similar to an apartment building or even a small town.You can exert a degree of security insofar as it serves the common good, but an absolutist approach of the kind you describe rapidly becomes self-defeating and unsustainable over the longer term. I might add that absolutism in this context refers to the idea of abolishing borders as much as to the idea of sealing them. After all, we have controls in between the borders of US states with limited powers to enforce prohibitions or requirements unique to that state, from carrying certain produce to wearing a motorcycle helmet, and these are not considered especially onerous.

Rather than abolition of borders, I see a trend away from a presumption of exclusion as the default and towards a policy of neutral vigilance - in other words, personal migration will come to be seen in the same light as other trade flows, subject to inspection and monitoring but requiring specific grounds for interference.

So, suppose you have a business importing silk from China, and the hacky part is that it's woven in conformity with 6502 assembler code or something. It comes into the US in a cargo container, and we all accept that DHS/CBP want to assure themselves that it doesn't include radioactive materials, smallpox, or marauding silkworm colonies. That done, we expect them to be indifferent to the question of whether 8-bit silken handkerchief designs will affect the US economy in positive or negative fashion - that's for the market to discover, not the customs inspectors, as long as there's no ongoing trade dispute between China and the US justifying their exclusion in accordance with treaty.

We already have such a policy in place for visiting tourists and businesspersons from other developed countries, and which is mostly reciprocal - you can grab your passport and fly to Japan on a whim for up to 90 days, and vice versa. Within both the US and the EU, the benefits of allowing migration between the individual member states seems to considerably outweigh the various costs; economics suggests that rational policymaking on international migration will go the same way sooner or later.

Of course, this isn't foolproof and the downside of such a policy is that criminals can exploit such openness to further their wicked ends. But insofar the number of such people/incidents is low - not least because more people appreciate the freedoms of the open model, and have a stake in its preservation - that risk is tolerable.