I actually do this in my classes. My department has an in-house written College Algebra text, but I recommend to my students as an "alternative" that they get Sullivan College Algebra, 8th edition, for about $5 online.
Two things with this: One is that potentially I could, like the professor in the story, get in trouble with my department for this arrangement (it's a bit of a gray zone). Second is that the college bookstore can't stock old editions from the publisher. So it's a one-by-one acquisition process. You can't depend that students have it on day one; therefore I have to provide handouts for the first few weeks before they get books. And if you did this across the institution, you would likely deplete available sources of the old editions (e.g., I allow one edition back of Weiss Introductory Statistics, and I'm pretty sure that I've single-handedly caused the depletion of it at Amazon -- I already need to keep exercise lists two editions back, which is a maintenance problem when I adjust my assignments, and further back than that and certain exercises have values changed or don't exist at all). Online homework is chimerical, IMO; college students students should have the maturity to do their own homework and then verify with odd-numbered answers at the back of the book; when I tried online homework in the past, it just threw up more technical barriers for students to say they couldn't do it.
So I agree with the GP that open textbooks are the way to go. OpenStax at Rice University recently upped their offerings quite a bit; not perfect, but finally over the threshold where I could work with them. I'm currently trying to puzzle out how I could switch to using their College Algebra and Introductory Statistics books, in the face of officially required in-house texts from my department.