I've never taken an actual SM class, but rather learned via SMing in college. (Which did give me tech credits, so it could be considered a one-on-one class with the faculty directors.) My directors asked me to include breaks even though breaks weren't an actual concern - I guess to get me in the habit of thinking about, and keeping track of everything.
My first director at my current theatre was Problematic about breaks, so I stuck to documenting breaks through that and haven't broken since. I don't know if anybody would complain if I stopped keeping track, but like EFMcMullen I record them by default - although I also have a small box in the header of my reports (among the other small ones, like "date" and "next call") where I write our unrounded break times. The work schedule does get rounded to the nearest 5.
To me, it's one of the many things I almost accidentally keep track of, and while it may neither help nor hinder, it would take me longer to remember not to record the breaks than it takes me to write them down.