I have pretty terrible hand writing, even when trying. Being a lefty doesn't help either. Letters are usually not uniformly sized. I make mistakes, even by my standards, and make messy corrections. Without a guide lines, a line dips or the size of the letters gets steadily bigger or the kerning is inconsistent. I can't draw a passably straight line to save my life.
Which is weird, because I'm artistic and have done plenty of work I'm plenty proud of. But there's something about handwriting, be it for something professional or something for entertainment (I like to make a lot of maps for table top gaming, and I like to put old timey writing on them, if for no one else's enjoyment than my own) where it never looks "comfortable." I can write super, super tiny or the equivalent of 16 point font, and it still looks rushed.
What I'm getting at is, as was said above, if you don't have good handwriting by now, by all means don't stop practicing or even doing it because you enjoy it. I still do a lot of hand writing because I enjoy calligraphy and really excellent hand lettering. But chances are your style isn't about skill or practice, it's about how your hand works and how your brain processes things. Like I said, I've done plenty of art and even tried my hand at forgery with some reasonable success. But when it comes to my own handwriting, it still looks like crap in my eyes. You can retrain that for sure, but you're doing it while working against what are now ingrained patterns.
Some advice: learn to gauge the tension in your hand as you write. I remember as a kid getting aching cramps in my hand from cursive practice. A lot of my problems with writing today still come from how I've learned to hold a pencil or pen over the years. Maybe your grip is too tight and it results in jerky pen strokes. Maybe your grip is too loose and your pen slips on you. Maybe instead of thinking about each line of a letter and "putting them together" (as I tend to when I'm writing in non-cursive), you need to establish flow. Or maybe instead of always trying to flow through a line, you need to be more deliberate and go slower with each letter.