I guess the question is, what will "citizenship score" actually do? And how will they measure mastery of the material?
As
@Dr. Sexbot and others have stated, it's been around for some time under various terminologies. My private K-8 school labeled this is as "Social/Emotional Development" and it was intend to reflect: (1) whether one was behaving appropriately for their age, and (2) if they were behaving appropriately with both peers and authority figures (teachers, playground aides, etc).
In the public high school, I attended, "citizenship" was assigned on a 1-4 scale with 1 being the best and 4 being the worst. Whereas my K-8 school gave one overall score, citizenship at my high school was assigned on a class by class basis and based on how one treated classmates and teachers. This led to some odd situations, though. As a freshman, an upperclassman in my World History class shared a story about the time he got marked down on an assignment in part due to bad behavior. After a parent/teacher conference where the teacher was told behavior wasn't grounds for a lower grade, the teacher updated the grade accordingly and he got an A for the quarter with a 4 (the lower possible mark) in citizenship -- pointing out the fact that students deemed troublemakers can still earn passing grades even if it seems paradoxical.
One big issue with citizenship scores is the fact they're based largely on subjective, intangible qualities. In my high school, someone who showed the same courtesy and politeness to two different teachers might get a 1 from one and a 2 from the other with no real explanation for the difference. Even if there was a rubric for citizenship, students are still at the mercies of individual teachers' moods and any biases they might have for or against certain students.
What the fuck is a "citizenship grade", and when I was in school most of this stuff was already done, Turn in an assignment a late (outside of being absent or being a good student (not necessary 'grade wise' but "good citizen") and fucking up once) 5/10% off your grade with the plenty going up each day its late.
In both grade school and high school, work submitted late without an acceptable reason was penalized. in some cases, work submitted too late was flat out refused. In college, what you mentioned,
@stupidpieceofshit, was more of the norm in that late assignments were penalized for each day they were late up to a maximum -- usually 20-25%.
Someone I know who spent time as an adjunct instructor in an art school made it clear on his syllabi that late work in that field not only was unacceptable, but unprofessional as it would irreparably damage one's professional reputation with other art folks and critics.
in the era of special snowflakes

and participation trophies, it's not surprising we have schools adopting guidelines to prevent hurt feelings in the form of poor marks for late work or bad behavior.
We all know those are two things the jogger population struggles with and removing those factors from the academic grade will serve to falsely boost their grades. Plus continuing to teach them that they can act like little savages and there are no real consequences for their behavior fails us all.
That's the thing I don't get. Just the other day, an activist interviewed by a local media outlet was pushing the end to the "school to prison pipeline." However, these various efforts to remove personal accountability and to de-emphasize the learning of meaningful skills seem to do more to perpetuate that pipeline than anything else because it perpetuates the myth that there aren't/shouldn't be any consequences for unacceptable behavior.