If we're screening for criminals/known terrorists/associates, then you'd need papers--otherwise, if people didn't need papers, we'd not be able to screen for anything. Also, presumably it's not the easiest thing to just fake the papers, or again the screening would be useless in general, and there would be no point in even doing it. If it turns out to be useless in general, then what are we even doing with any border security at all, aside from checking bags to make sure that criminal items--like bombs, endangered animals/animal parts, etc.-- aren't being brought in just then? (Which by the way, I'm okay with checking, but I forgot to specify that)
But, let's pretend that, say, it's easy to fake the papers for the child trafficker, but not for other stuff.
I would just let the child trafficker with good faked papers go through, yes.
If we were talking about a child trafficker moving a kid from Belle Glade, Florida to Jacksonville, or even Newark, New Jersey to LA, then of course they'd not need any papers whatsoever. Nobody's checking anything there. Nobody's screening anything. And I don't want everyone checked whenever they travel anywhere.
I can see some merit to checking or screening people occasionally (such as when they cross a national border) to try to catch some criminals or terroristic threats, but I'd be far more easily persuaded to not even do that than I would be to force people to be held while we check their DNA just because they're traveling between countries rather than across the street or from city to city or state to state.
Just for background, by the way, I consider myself a "libertarian socialist." On the libertarian side, I'm basically a minarchist. The socialist stuff comes from disagreeing with the libertarian embrace of free-market capitalism as the official economy. I'd institute a very different, government-overseen system where the competition for scarcer resources is based on providing both the basics for everyone and the things that people want, which we'd learn via regular polling. I'm kind of a laissez-faire hippie, with the hippie side being attracted to helping people other out communally. Re borders,I think that ideally, we wouldn't even have different countries.