Some people naturally have beautiful handwriting, others struggle to make theirs legible, never mind neat. Children can spend a long time at school practising handwriting and being criticised if it isn't neat enough. Is it important for handwriting to be neat?
It's better if it's legible, as sometimes that makes a big difference in the workforce. Doctors and nurses need to be able to read patients' charts, order forms for businesses need to be legible, customers need to be able to understand signs (not that they read them anyway) etc. Just legible though. It doesn't need to be "perfect" and sometimes a difference in style is mistaken for a lack of care or neatness. I've lost count of the number of times someone from my parents' generation had a go at me or others of my generation for writing in the handwriting style we were taught instead of the copperplate they are used to. It's comparing apples and oranges and it's a bit rude.
My Mother always had the most perfect writing.
She told me back in the 'old Country' she was taught by a Gypsy!
Mother has to write over and over the words, till they were perfect.
That was back in 1918.