My parents are both left handed. Mum’s handwriting is very classically neat according to a standard form with fairly wide letters. Dad’s is not classically neat, favouring taller letters and shapes more angular than rounded, but it’s definitely tidy and very legible.
Another of the neatest writers that I know is left-handed. (And female. I have observed a moderately strong correlation—though by no means uniform—between classically neat handwriting and being female.) I can think of several other left-handed people that I know, but I don’t know their handwriting. My left-handed grandmother’s handwriting is neat in the fairly illegible cursive style of the era, but she does it with her right hand since they beat left-handedness out of you (in handwriting at least) in those days.
(Fun fact: I and my seven siblings are all “failures”. Consensus seems to be something like 20% chance of a child of two lefties being left handed, so the probability of all eight of us being right handed was somewhere around 17%.)