What about this makes it a pain point? Is it the amount of time that it takes to deal with cheating, the inability to effectively punish the behavior, the impact it has on the professors' (and perhaps some students') morale, or something else?
The course has to be designed with cheating prevention and detection in mind. So: some things you want to do are not possible. Takes significant extra time to develop course materials (cannot reuse previous years’, may need to shuffle questions and answers on tests, etc). Trying to make sure questions are not easy to google/GPT. Time spent dealing with cheating and consequences, e.g. determining if cheating happened, collecting evidence to present to honor council.
You nailed all three. But to be honest I think the time spent would be viewed as the worst.