Is it possible to craft a course that assumed that students would collaborate/copy from each other and the internet while completing any take home assignment (so homework and projects but not in-class tests), allow for it explicitly, and still teach as much as the existing courses would have if students didn't collaborate/copy?
Yes, absolutely possible - it's just a lot more work. As simonsarris points out above, this will be the exception rather than the rule in a system where universities and faculty are not measured/rewarded for quality of teaching.