Ditto to everything aeh said

Plus I'll add that with drawing, you aren't having to recreate something learned, and your pencil doesn't have to leave the paper often like it does when you are, ahem, drawing letters (which is what dysgraphics do). My 15 year old dysgraphic ds will tell you (as if it's as normal as sunshine) that he likes writing numbers better than letters because there are only 10 numbers you have to memorize how to draw, and there are more than twice as many letters. That same ds, who has had remediation and OT for handwriting, has handwriting that looks the same as it did in 2nd grade, when it didn't look very good. When he uses handwriting, he writes at about the same speed as a 2nd grader even though he's in high school. Yet he is an amazing artist and loves to draw

I've done some reading up on dysgraphia and other disorders that affect handwriting, and am curious about something. Would it be surprising for someone with dysgraphia to be good at art/drawing when working patiently in an unstructured setting? To have decent drawings, but all text surrounding it to be difficult to read, letters poorly formed and widely spaced, and unable to organize text very neatly on a page, unless copying their own work painstakingly? I just wonder, if one is dysgraphic, would they dislike creating art?
This goes with mentions of feeling slow with writing (and thus feeling hurried and being more sloppy, or writing less thoroughly than they're capable of expressing because it would take too much time to write more)
This all sounds very much like dysgraphia.
and not understanding criticism of their 'neatness' (feeling insulted that it's not readable to others).
This, of course, is going to vary from child to child based on personality, but if a child has dysgraphia that goes undiagnosed and unaccommodated, it leads to the potential of great frustration, anxiety, loss of self esteem when comparing their work product with other students at school.
Basically, at what point is it considered a poor handwriting ability (or brain too fast for hands) vs a problem that necessitates intervention/accommodation?
It's not that there's a "point" at which sloppy handwriting becomes sloppy "enough" that it's considered dysgraphia. Dysgraphia isn't an issue of sloppy handwriting, it's a neurological-based disability that impacts the ability to develop automaticity, which most frequently shows up as an inability to master handwriting. If you suspect your child has dysgraphia then the next step is to have him/her evaluated. If he/she has dysgraphia, you'll want to get accommodations in place as well as some basic remediation asap. If you're still wondering if it's something to wonder about rather than act on, ask yourself this question: if you suspected dyslexia, would you ponder at what point difficulty reading becomes dyslexia or would you have your child assessed for possible dyslexia?
What you've written above sounds very much like potential dysgraphia. You can also look and see if you see other potential dysgraphia signs: poor pencil grip, awkward posture when using handwriting, uneven pencil pressure on paper, refusal to do written work, wrist pain, holding wrist or elbow while writing, letter formation etc not improving at the rate of school peers, letters or numbers reversed or switched, etc. You can also ask your child to write the full alphabet, upper and lower case. Time them while they are doing this and watch how they form their letters. Are they starting most of the letters at the top? Do they seem to have to stop to think about how to write any of them? Do they remember how to write all of them or do they make mistakes or reversals? When they are finished, divide the # of letters written by the total # of minutes, then google letters per minute rate for your child's grade or age. Does your child's result seem low?
What happens when your child has to write a sentence or paragraph? (I'm not sure how old he/she is so I don't know what ability level for writing they should be at.. but if they are far along enough in age/grade to be composing sentences and paragraphs think this through) Does he/she spell correctly when writing? Use punctuation correctly? Use capital and lower case letters correctly and consistently? Does he/she form letters the same way every time or not? One of the biggest impacts of dysgraphia is that working memory is all devoted to figuring out how to form letters while writing, so there's nothing left over for thinking about proper spelling, punctuation, etc. Which leads to my last question - is your child's written output equivalent in quantity and detail to his/her verbal output? Dysgraphics tend to have a notable difference.
If he/she is dysgraphic, you'll want to start accommodations and possibly a few interventions/remediations depending on your child. Dysgraphia isn't something that dysgraphic outgrow or that goes away someday. It *is* something that is easy to accommodate, especially in our modern world where there are keyboards everywhere

Best wishes,
polarbear