I bought a nice fountain pen (well, a $14 pilot) and overhauled my cursive writing. It took about 6 weeks and I write pretty legibly in cursive. I'm more legible in various print scripts (that I have also worked on as an adult), but cursive is faster.
Admittedly, that is just an anecdote. But if you're curious, try and get better... you'll likely improve if you actively practice.
I never liked pure cursive and do a mix, it's more of a print-sive where some letters are always print (F, J, G, Q, a couple others) and others are cursive depending on flow, speed, etc.
I have a bit more practice because I also sketchnote.
Have you tested? I recall - maybe a decade ago - seeing a study suggesting that in fact printing individual letters could be faster; I still write in cursive when I need to handwrite though (basically never).
Edit: http://nautil.us/issue/40/learning/cursive-handwriting-and-o... is a good summary; first 2 paras of last section are the TL;DR.
Ideally, I suppose I'd have an accurate transcript and I could just take time-stamped notes that could key to that transcript but that's not the reality. (I know I can record audio but, in practice, going back to audio after the fact is just too much work for most purposes.)
Longhand notes (which I do frequently for the RPGs I run, so practice isnt the issue) are nigh unreadable. I literally have dozens of notebooks (not full, but at least 30 - 50 pages each is pretty common ) of notes I struggle to read and organize.
Being able to write with speed and br able to read them is why an elementary school teacher recommended that I try using a computer to write on back before laptops were a thing, and it remains a big reason I rely on them for work notes now.