There's a big difference between "cannot" write neatly and "chooses not to." It sounds like your DD is in the second camp. It does take more time and effort to write neatly, and when your brain is working at 1,000 wpm, that's torture.
My DD9 had the same issue at your DD's age. She had been writing beautifully at 3-4 (better than I ever did), and then started turning in slop at school. We intervened by telling her that she didn't have to write perfectly, and we understood the desire for speed... but "good enough" is only good enough if someone else can read it. Thereafter, if she did a homework assignment and we couldn't read it, we'd make her rewrite it. That taught her to put in enough effort to get it past us the first time.
She was having similar issues with rushing through her work, too (not reading instructions fully, sloppy mistakes in math, etc.), so we instituted an incentive where she can earn a few additional dollars when she brings home papers with As and Bs on them. It's got her paying a lot more attention to the quality of her work, and has been very effective.
