What is the transaction being made by paying tuition at most US colleges/universities? Are you paying for the time spent teaching, the price of education/intellectual property, or the diploma itself?
More specifically: Assuming it is not being repurposed for profit etc, is the IP covered under fair use? If so, could a person auditing a class simply for the sake of learning legally take classes without having to pay tuition?
There are two kinds of universities in the US: public and private. The public institutions are tax supported, though not completely. The private universities see to their own funding. Public universities are governed by rules defined by the individual States with some regulations at the national level and some left to the university. Private institutions have some regulations, but largely make their own decisions.
A university is an expensive place to operate. Even public institutions get only partial tax funding. Tuition is designed for two purposes. One is to have the students contribute financially to the costs, but the other is to provide an incentive for students not to waste their time and, by their presence, deny opportunities to others.
There are other concerns besides money. Your presence might not be welcome on a campus if you are not affiliated with it simply for security reasons. Trying to sit in on courses without permission might well result in a court order keeping you off campus. This is rare, but it happens. Your presence would then have legal implications.
As to the IP question here, there is nothing special about being a student vs a non-student with respect to IP rights. Students as well as non students have the same fair use rights. But note that such rights are limited by (varying) laws.
No one would be likely to get upset of a registered student shared their notes with you. You could use them to educate yourself. But neither you, nor the student could, for example, republish them.
Most universities have rules about auditing. They may permit it at lower cost than a "matriculated" student, since there is less paper work, hence lower costs. You get an education, prodded you do the work, but you don't have a record of it. But it isn't "free" in any sense. Space in a classroom costs money, both directly, and indirectly since a seat occupied by one person isn't available to another.
Even in COVID times, when physical space isn't a factor, the ability for a professor and other course staff to handle students effectively is limited.
To be explicit about another of your questions, what you are really "buying" with your tuition is opportunity. Opportunity to learn under the guidance of experts who have the perspective to know what is important in their fields. Some students pay tuition and don't really take advantage. Sadly. But freeloading off of the system will deny opportunity to others who might benefit and be more willing to participate fully in the system.
Let me give a bit of other perspective. I'm a Tai Chi student and instructor. The art, as a martial art, is about 800 years old, though the principles are much older. We have a tradition that we don't teach for "free". We believe that we are giving something valuable to our students and so require something valuable in return. In China, in the old days, it might be a dozen eggs, or service on the family farm, but something. Again, this is for two reasons. One is to support the instructor, but, more importantly, to incentivize the student to think of the instruction as being valuable.
Another thought. There is currently a move underway to make university education, up to some level, free of cost to the individual in the US. That doesn't make it free, as tax monies would be required to take over a much larger share of the burden. I support those efforts, but the question about student incentives under such a system is something that should be considered. The current system, however, is blatantly unfair since the distribution of wealth in the US is so unbalanced. Hopefully we can work this out.
Frequently, material from courses is available to all for free. For example, you can take Benedict Gross's course on abstract algebra, Michael Sandel's course on justice, or Jim Hefferon's course on linear algebra. All have reputations as outstanding instructors, and these are just three of many examples.
Auditing a course means entering into a formal relationship with the university -- i.e., paying them. If you do this, and perhaps if you only unofficially "sit in" -- then the professor might be willing to give you feedback on homework, and/or to answer your questions. This will probably be at the discretion of the individual professor.
This is very worthwhile -- but there may be appealing options available for self-study if you can't or don't want to pay.
