If we actually want people to learn, plagiarism detection isn't the problem, it's the industrial factory approach in the first place. Get rid of that, and instructors can know and talk with their students well enough to tell what they actually know and understand instead of having to rely on artifacts that can be faked.
But we'd have to be spending more money in the first place, vs spending money on other things (like cops?!).
Effective writing is an important skill, so I don't think in-person conversations would replace papers, but from a conversation with a student who plagiarized their paper you could probably tell that they didn't really understand what they "wrote."
I think of it like stack overflow. If someone borrows ideas and code from there for a code review, I'm fine with that, as long as they understand how the system is doing. Being able to do research and find information is a useful skill! But only if it's applied correctly, with understanding. So I'm going to probe on that. And it might be blindingly obvious to me that they didn't understand what they were doing, or why the pasted code isn't appropriate. And I don't need a "stack overflow detector" to see that.
"Interpersonal skills are optional" is not a good side effect of our current educational system!
a) Can't actually explain what they were writing about
b) Didn't learn how to correctly cite things, and/or don't understand what plagiarism is
Are plagarism detection tools perfect? Heck no. Lots of false positives, and of course they don't do anything for essay writing services (unless, of course, the service plagiarizes - which happens!).
Under the ToS of all plagiarism detection software (at least that I've looked at), the student's work is added to the corpus against which all texts are tested against. This is what you would _obviously_ do if you were building a plagiarism detection app, however that means a student is forced to submit work to a private company, which will then profit off of their work.
You might say what the value of a gen ed term paper is to a student, and I'll agree it's not much. But that's not the point. The student is forced to provide that to a third party by the school, which will then profit from it. This isn't a Facebook-like situation where you can just not make a Facebook account. I would guess in many schools, refusing to submit to plagiarism detection software would be taken as evidence of plagiarism.
This is probably a few years out of date, and I see that Turnitin recently shut off their 'upload your own work so you can see if it's plagiarized' product, but for a student to have an active defense against plagiarism _costs money_. Yes, if a student wanted to make sure their paper wasn't accidentally plagiarized (this is common, because their algorithms are shit), that will cost a few dollars. This is unacceptable.
And for anyone who says, 'just transfer sections to a prof that doesn't use the software', there are contracts with entire departments and schools, which then force professors to use the software. Yeah, you could transfer _schools_, but the point stands.
Plagiarism detection software -- which purports to support the intellectual property of the author -- does just the opposite.
Also, I should mention that if someone wanted to cheat, they wouldn't plagiarize; they would simply get someone to write a paper for them. This service is far, far more common that you would believe.
When I was in school students did plagiarize a lot. It went out of style as software was introduced. I distinctly remember the panic'ed buzz as students discovered the teacher (or professor) was using detection software. The services you're talking about are common precisely because of plagiarism detection software.
I'm not disagreeing with your points about morality of it though, just the efficacy.
Adversarial teaching environments are a symptom, not the problem. And the fundamental issues don't have a clear solution, though it is clear that the situation is far from optimal.