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.