A book is usually open in front of me with a pen at the ready. An application.. well it depends, but best-case scenario is that it's in a easy-to-switch-to window and is natural to just get the idea down without jumping through hoops.
As an aside from a sufferer of ADHD, I think Augmented Reality tech would be a killer platform for an in-place TODO/Note/Reminder/assistant.
I would agree with what you've said to a point, but this kind of statement needs expanding.
For my wife and I, we're using Wunderlist (bought my Microsoft in 2015) and we can assign things to each other, star them as important, comment on tasks, leaves notes, set reminders, and so on. It's a... wunderful (har! har!) app and so far it's UI doesn't get in the way. I'm just waiting for the moment we hit the limitations of the free version and have to spend nearly AUD$130/user/year (USD -> AUD) to maintain its place in our household.
Platform issues and friction is far too high. Even just loading up the browser, or context switching to a different tab. Plus... if your work is of mathematical nature, it's an added headache.