More to the point, even if you type fast enough to transcribe the lecture (or you know steno or pen shorthand or whatever), transcribing simply doesn't do the job of note-taking. (I speak from direct experience -- I did audio transcription work for a few years, and I generally wouldn't have been able to pass a test on something I'd just finished transcribing, even after having gone back through to do proofreading/editing at the end. There was some degree of mental engagement with the substantive meaning of things in the moment, but it was largely a "pass-through" sort of activity, if that makes sense.)

The idea isn't to merely take down a record of what was said, but rather to integrate the concepts into your own understanding: What associations can be made with existing knowledge, can you demonstrate to yourself your understanding of an abstract by contriving examples of it, can you explain it to your grandma, do you have a clear model of its scope/boundaries/limits and of where it fits into its domain, do you know the why as well as the what, etc.

The part where we have to condense what we're hearing into something concise enough that we can keep up is a feature. For that reason I wouldn't really recommend transcribing the lecture and then making notes out of it later, either (ideally we should be reviewing and organizing the notes into a more structured / fleshed-out / pared-down (as needed) form later anyway, so it would just seem to add an extra step). I don't know what everyone's courses are like, though, so maybe that approach could be useful or necessary for someone.

(And of course the takeaway here is that, assuming my understanding of it is well-grounded, and provided there isn't truly something inherent to handwriting that makes it cognitively advantageous, typing should have the potential to be just as workable a medium.)