Welcome to matheducators.SE! It's great to have an undergraduate student participating in the site.
The question is basically written as if this were the year 1996, when I started my teaching career. Today, we have the internet.
Your question includes a lot of money-related material. There is no fundamental reason why students need to keep getting financially exploited by the textbook publishers. For the undergrad math and stat courses you're talking about, there are generally multiple free options on the internet. Most instructors just don't care about the economic victimization of their students. They've gotten used to using a particular non-free textbook, and they're not going to change now, because it would be work.
Your question is written as though the mechanism for economic victimization were still the cost of the books, but this is no longer true, because you can get your book for free on the internet at http://libgen.rs/ . For lower-division math, the mechanism for economic victimization is no longer the cost of accessing the book, it's the cost of an account on a system like mymathlab. Again, there are nonexploitative alternatives (e.g., WeBWorK), and again, most instructors don't use them because they're used to using the expensive thing already and changing over would be work.
Your question is written as though instructors could still keep secrets from their students:
Instructors can assign exercises from another book, without divulging their choice of textbook to students.
This won't work, because the internet exists. If your instructor assigns you a problem, and you don't know what book it's from, cut and paste the text into a search engine. The first hit will be on chegg.com, your central resource for cheating and copyright violation.
And finally, your question is written as though it still made sense for teachers to be assigning problems for points and making those points enough to have a big effect on their students' grades. This does not make sense today, because students can easily get solutions from chegg.
I'm the author of some free physics texts (and also one free math text). About half of the problems have already been illegally copied onto chegg, and have solutions available there. Because of this, I've given up on using homework grades as more than a feedback and progress-tracking thing. (I count them for 1% of my students' grades.) My students check their machine-checkable answers using free sotfware, and I grade their non-machine-checkable answers by hand. After that, I email them solutions.
Your question is somewhat helpful in that, although I don't agree with almost any of your logic, you made me rethink whether I want to simply put the solutions in the books at this point. I don't see any significant benefit to doing that, except perhaps for some small number of students who are using the books for self-study and can't get an instructor to comment on their work. The downside is that many of the people using my books don't agree with my opinions and therefore are still giving 10 or even 20% of their students' grades for homework. Those people would probably be very upset with me and stop using my book.
For your own education, given the reality of how the courses you're taking are being run, I would suggest that you simply work hard to solve the problems without access to the solutions. Get going far enough in advance so that if you get stuck, you have time to get help. You can get help by going to your TA or instructor's office hours, or to an on-campus tutoring center. If you want examples with solutions, use the examples in your textbook -- most commercial texts have a huge number of these in every chapter.