You're talking about someone taking notes on an iPad Pro instead of paper in order to improve his study efficiency; it is way different than someone playing Crossy Roads while you teach.
So, what's wrong if a student records your class? I am seriously asking, not trolling. I would like to record your class so that I can play it back in the car instead of listening to a song by the Beatles for the 100th time. What's wrong with that? You, as a teacher, wouldn't know the difference.
I've mentioned previously that it's annoying to people around you. You're arguing that prof has to provide a reason to you why something is allowed or not. The answer to that is no they don't. This is my point about accepting it and moving on. Prof either says okay or not and that's the end of it. Your perception of the impact is neither here nor there. In the working world, if a supervisor tells you some rule or whatever and you try to debate/discuss then be prepared for short shrift. I'm not sure you fully understand the point yet.
well-rounded education starts earlier. At 18-20-25 you better have a well rounded education by yourself, and learn how to keep it. College and University are for specialization and workplace preparation. If by 18 you don't know the US system you won't learn it thanks to a college class that is forced upon you. Granted, class availability should always be good and if an engineering student feels compelled to learn some music theory then he should be free to do so.
Any engineering school that doesn't provide you with well-rounded education is short changing you. They have no idea the level of quality or otherwise that your high school provides to their students. The whole point of Calculus 101 or 201 or whatever you might consider a waste of time is for several reasons, such as, a refresher course, a leveler course for different high school methods which teach topics different ways, or just to weed out the underachievers.
There are too many high schools nowadays that use grade inflation to the detriment of their students, or allow poor teachers to hide within the confines of school walls, or just are in places which corrupt the minds of kids (e.g. Texas). You have to get core subjects before specialization.
Equally, if you find repeating classes a drudgery then that's also a heads up that your attitude stinks if you don't excel in areas you claim proficiency. Life is full of drudgery so better you get the opportunity to right your attitude in education still.
You forget one important detail. You are their servant, not the opposite. They pay you for a service, you provide the service efficiently. Babysitting is not part of such service agreement.
No, professors don't serve you at all. You're totally wrong there and until you grasp that a student is just a statistic then you won't get it.