Every essay I wrote, I'd always force myself to reach the max "12.0" grade level. While writing I'd struggle over word choice, sentence structure, rearranging paragraphs, working on my tone etc, all in pursuit of the 12th grade way to phrase things. All my revisions were subject to the approval of the Grade Level checker.
Whenever I could I would check the grade levels of my friend's writing - usually by showing them a "neat feature" they could enable. Then, I'd smugly applaud myself for being the better writer whenever their grade level was below 12.0.
The Grade Level feature fascinated me and to try and master it, I found a book about Microsoft Word and looked through it in a bookstore. I was absolutely gobsmacked at how simple the formulas was. I had childishly been expecting something, like perhaps Utah educators imagine they have. I genuinely expected the method to be complex beyond my understanding.
Instead, Word used a variant of Flesch-Kincaid. There was a direct relationship between sentence length and grade score, and polysyllabic words and grade score. Meaning, the longer your sentences and words, the higher your grade score.
As soon as I got home from the bookstore I loaded a draft of something I had written. It was "pre-12.0" writing from me. I simply deleted all the periods but one and checked again. 12.0.
Automatic grading is a wonderful lure. It's nice to imagine that there's some objective writing quality easy to tap into. At the moment, I think we're far from that ability.
Personally, I feel the solution to insufficient teacher time is to use peer grading much more, and spot checks. Get kids to read and revise each other's works frequently, and teachers should aim to grade at least N papers per student where N is much less than the number of papers a student writes.
Revising is a really vital part of writing. Getting more chances to do revision, plus having to write something good enough to show your peers, plus having the risk of any paper count for your grade should compensate for incomplete teacher grading.