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!
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?!).