I went to grad school many years ago and even then it wasn't uncommon for students to record parts of the lecture. I've done it many times. Back then I had used Word on a MacBook, which had an awesome notebook feature. It allowed you to record and tag the recording with a title. You could skip to a specific part. All within the written pages you had with tabs on the right hand side for different classes or subjects. It was really great and especially helpful when complex topics were being discussed. To my knowledge, no one ever used class recordings for any purposes other than to study. I wouldn't worry too much about it.
Couple things. First, many people have pointed out that the in the good ol' days, many people used a cassette recorder to capture lectures, and boy wasn't I naive to not know it. Of course I realize that (after all, I was a student for a long long time). There were a couple grad courses that I myself recorded (with a 3rd generation iPod with mic attachment). The recordings were made when I asked the professor, who in turn asked the room if anyone minded. They did not. The recorder sat on the table in front of the instructor. Everyone saw it, any time it was in use. And those files were a shared class resource for everyone, with the blessing of the instructor.
Now, a key difference between the old tape recorder era and the modern digital recording era is that I could very easily make those recordings available widespread and wholesale all over the Internet. That would include more sensitive class meetings like a post-exam review. There was always a way to share recordings, but the scale and scope was much different in the cassette days. That's worth acknowledging.
But the other, bigger issue for me is that pedagogical methods have shifted, particularly in higher education (long the domain of the "sage on the stage" lecture-heavy all-knowing professor). That's considered a pretty outdated model these days. Classrooms these days are supposed to be student-focused, rather than instructor-focused, so the recordings would not be capturing what they would have in the olden days. Having captured a recitation of facts on tape wouldn't do too much good on my assessments, because recall of trivial detail is about the least important thing to me — I'm more interested in assessing your ability to apply that knowledge in a context you've never seen before (and I'll probably give you those trivial facts and equations so you don't have to try memorizing them — I want to see if you known when and how to use them). It's a more authentic experience to "the real world."
If I were just gathering students together to rattle off a series of trivial facts and equations, distilled and condensed down from their textbook, then I could see all sorts of benefits to recordings (and I'd probably provide them myself). But that's not how I generally operate in the classroom. There are all sorts of better ways to deliver the trivial detail outside of the classroom. When we get together as a group, it should be to do something that takes advantage of the fact that we're all in the same room together. So classroom time for me is more used for applying the knowledge in problem-solving activities or lab experiences that students work on together in small groups as I facilitate. Frankly an audio recording of that wouldn't get you very far.
And finally, the classes where recording makes the most sense, as I suggested above, are courses in which facts and details are just rattled off in lecture. What about those courses that don't lend themselves to that format? I kind of straddle a few different disciplines, and one of the courses I teach is about educational methods. The course is very discussion-oriented and covers sensitive topics (bullying, racism, sexism, LGBT issues, disabilities, etc.). For that class to work as it should, I really have to build up a rapport with and among students, so that they feel as though they can just speak the unvarnished truth that's on their minds, and we will respectfully hear their point of view and discuss it. Some of the students share very private and personal experiences and opinions that are germane to the topic at hand, and it's really what makes the course so useful and so powerful to others in the class. These are generally senior-level students who are beginning to talk to one another as professional peers rather than just fellow students in a class. If someone were recording all that? Wow, what a breech of trust, and what a chilling effect it would have on the important discussions that happen in that classroom. And just so there's not misunderstanding — I really am not concerned about someone secretly recording what I have to say. But I do worry about my students being recorded, unknowingly, as they share things about their teaching experiences or things that they went through as a student. Some of it is mundane, but when someone starts talking about being called a particular racist slur, or instances where teacher acted inappropriately toward them, or about physical or sexual violence at home, or coming out, or countless other things, can you imagine the chilling effect and betrayed feeling someone would have about being recorded without knowledge?
But those kind of classroom experiences are the real power of a good college classroom. It's what you don't get just sitting around watching YouTube or listening to recorded lectures on iTunes U or wherever. As far as I'm concerned, a teacher is not ready to be sent out into the world until they've really had and heard those kinds of conversations. So it's important the the discussions happen, but it's just as important that they don't become the seed of embarrassment, harassment or worse.
So, that's where my problem lies. If a student records me unknowingly, I'm not worried that something bad is going to happen to me. I am conscientious about what I say to other people and really have nothing to hide. I'm tenured and secure in my career. I've also had years to unpack and process my own hang-ups and be comfortable in my own skin, so it's not a source of anxiety for me. But I don't assume that to be true for my students.
I have had students make recordings of class (either as part of an ADA accommodation or just by their request), but it's always been something that is known to the entire class. If something comes up that I feel just should not be recorded, I give instruction that the recording must be shut off (but nobody else in the room cannot take written notes during that time, to keep the field fair). But it is a betrayal of trust to not give every single person in the class forewarning that what they're saying is being recorded.
So anyway, tl;dr. Recordings make a lot of sense for certain kinds of classrooms (especially classrooms of yesterday), but a lot of well-designed learning experiences don't lend themselves well to recording, and some just absolutely shouldn't be recorded. We are becoming too accustomed to giving up too much of our privacy and personal agency already.