FWIW, my 12 year old DS in year 7 has appalling handwriting, which has been a problem since Year 2. At parents' evening recently his English teacher made it quite clear that it is an issue and will cause problems in exams. But I suppose you know this already? If I was marking papers and one was illegible I'd be inclined to make less of an effort to read it.
In yr6 his teacher made a real effort to improve it (for the SATS, I guess!) and that seemed to work for a while. She made him write clearly even if slowly, in the hope that it would speed up as he became more used to writing like that. Anyway, it's back to where it was.
At home we set him handwriting homework, where he has to copy a few paragraphs out of interesting books/newspapers. But we need to be more consistent. DS has hyper mobility which may be contributing.
He has those Stylo pens (the new gel pen) but prefers to use his fountain pen.
So in short, I am anticipating that handwriting is an issue because, as DS's teacher said, he could be extremely clever and do extremely well -but who would ever know, because they can't read his writing.
In an ideal world I think it is something the teachers should address, but in reality how much time do they have?
Why is your DS's handwriting so bad? If you can identify what the issue is -writing too fast so not forming letters, or certain letters being joined up badly, or pressing too hard so ink splatters, or just too small, or getting smaller as he gets tired, etc -then maybe you can start to help him improve it.