It's not just a function of the average conceptual speed of the lecture, either, it's also a function of how bursty it is, and both are relative to what you already know and modulated by the quality of the presentation.

Taped lectures are a game changer because you can 2x over the slow parts and dwell on the bursts.

And that's been my experience as a math student. Professors of advanced math courses tend to write very quickly for brief bursts and then pause to explain what's going on. The definition or proof they describe can often be subtle enough that you don't have much of a chance to understand it unless you've had the opportunity to preview the lecture notes before class.

Tragically, not every professor provides lecture notes in advance, and some don't provide lecture notes at all. Then if you're taking notes by hand you're taking a big risk that you might pause to reflect and miss noting a crucial step in the proof, leaving yourself baffled by what you wrote later on.

If you look at the paper sheet, it is because you have to check you are still on the guideline.

However I believe that at uni, I would write a whole line without looking if I needed to (that's after about a decade of fast hand writing almost 8 hours a day, 4-5 days a week, though). That those lines had a tendency to go up or down was not a problem, because making a clean copy of those notes was part of my learning strategy.