Has the school actually done handwriting with them, or have they expected them to pick it up by osmosis?
For my dc, I can see the difference handwriting lessons have made. (all at the same school)
Dd1 had lots of handwriting lessons-homework (1x a week) was often to do with handwriting, they did it in class 1-2x a week too. At the time I thought it was a waste of time-but now she has the most beautiful handwriting that is often commented on.
Dd2 they sort of mentioned they'd like them to start joining up in year 2, and showed them how to. No handwriting practice or anything like that. Her handwriting is like a spider crawling through the ink even when she's trying really hard to make it neat.
Ds has gone the cursive handwriting route. They started it at the end of year 1, and have done a certain amount of practicing it in school. He hates writing, and would choose not to do any, but he is developing (he's year 2 now) a beautiful style. I think give him a year or two and it will look as good as dd1's.
I also see how it effects dd2's work, she gets things wrong because she misreads something she's already written, or because the answer isn't clear (especially in maths). It also means if she goes to look up something she's written earlier it's so much more effort because she has to decode it first. Looking back, I wish they had continued the effort they made for dd1's class on handwriting. Difficult to unlearn now.
I wouldn't go the typing route. Because, at present, he will have to do tests/school work/exams by hand. Our local secondary had provided all pupils with a laptop in years 7-11 which they did all their work on. They've now reverted as they found they were getting to exams and finding their pupils were struggling with producing it by hand.