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> And yet, since we moved to Denmark 3 years ago, every time we've returned to Denmark through Padborg, we've been met by border control

Sorry, but that's just business as usual. Document checks on trains have continued to be a thing despite Schengen since its inception, and are even common on commuter lines. I don't have any hard numbers on their effectiveness, but it's not unusual to see people being detained as a result (which is risky for the detaining agency, as mistakes are quite costly), so I guess there is a net positive there?

Note that, from a passenger PoV, these checks usually consist of "vaguely waving your ID card at the officers passing by" (i.e. less effort than having your ticket checked, which involves interaction with an RFID scanner...), which makes this ominous think-piece even less convincing.