For me the main benefits of the tablet are:
- Copy/paste/drag. Pretty helpful when you manipulate long expressions, or want to condense a bunch of scratch work.
- Relatedly: easy erase. When I used real paper, pencil was too low contrast, and “erasable pen” never worked well. So I used a real pen and just crossed tons of stuff out; ugly.
- Keep a decade of notes with me wherever I go. (And cloud backed up so I won’t lose them.)
- Infinite zoom and no page boundaries. Seems silly, but it’s really nice to write as big as I want without worrying about running out of room on the page.
- Text search of handwritten notes. Works surprisingly well.
- Easily switch to different colors. 99% of the time I only use 2 or 3, but I find it helpful to visual distinguish the main argument/computation from “side commentary”.
However, the app ecosystem is lacking in terms of interoperability, feature completeness within one app and export/import capabilities, and there is nothing you can do about it in iPadOS. File management is pure pain unless you fully bought into Apple already.
It's very nice for brainstorming and making transient personal illustrations while learning and working through technical problems, but you won't get the feel and certainty of a physical notebook as an institution for persistent notes.
The iPad is way too expensive for what it has to offer, in practice.
That said, without its artificial limitations it would be the last computing device you'll ever need. It could be everything.
Disagree on permanence. My notes are useful for much longer when they can be electronically sorted, searched, backed up, and when they take up no additional space in my backpack.