It is not appropriate to withhold material from a student for failure to sign an NDA. That said, it is appropriate to remind the students of the value of intellectual property, and that they are not the copyright holders of the provided material.
By way of explanation -- the work at issue is protected by copyright. There may be some debate about who is entitled to the fruits of that copyright, the author or the institution, but many US institutions will cede to the author. In any case, it is NOT the student.
The way this is handled at my institution is that it is covered in the Academic Honesty policy.
The sharing or distribution of course materials for purposes of giving
or gaining unfair advantage in a course is prohibited. Students must
further respect the requirements of copyright protection for materials
that are made available for instructional purposes.
All the students read, and sign, the academic honesty policy upon entrance, and generally receive reminders at each course on the first meeting. Also, if the prof has any non-obvious course policies on honesty, such as how students are allowed to collaborate on teamwork, this is also shared on day one, as well as in the syllabus.
Thus, any unapproved sharing of lecture or other material is treated like any other violation of academic honesty policies. There is no "Cease and Desist" to the student (but any site hosting the material might get a request to take it down, and if non-responsive, might well get a Cease and Desist, or it's equivalent), but there may certainly be ramifications. For example, if the student has a previous major violation on record, such as cheating on an exam, a case involving unauthorized sharing might even result in separation (though a lowering of the course grade or failure in the course might be the more likely scenario).
I don't know that this would preempt the professor from pursuing independent legal action. For example, if a professor spent five years writing a textbook for the publisher, and found the entire preprint online prior to publication, and had real financial damage, I don't know if university policy would preclude a copyright violation lawsuit.
To summarize, the work is already protected by copyright, whether an NDA is signed or not. Asking students for an NDA, and refusing to distribute material to students unwilling to sign, is inappropriate. Some universities (maybe even "many") include copyright violation in their academic honesty policy, and students might experience penalties for traceable violations. There is also a possibility that students may be subject to the same legal actions that any copyright violator is exposed to.
Addendum: The University of Maryland has had their lawyers write up a treatment, which largely confirms my assertions, at https://president.umd.edu/faculty-course-materials-strategies-dealing-commercial-use. The situations where this comes up most often of late is when students upload course materials and exams to services like CourseHero or Chegg, but all the concepts apply for any unauthorized distribution of copyrighted material.