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.
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.
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.