To a mild degree, I don't think the school's idea is a bad one. The problem is that it doesn't account for the difference between a student who fails to turn in 20% of assignments and a student who fails to turn in 80% of assignments. When I was in middle school, my home life was fucked by several deaths in the family and parental separation and divorce, and I frequently was completely unable to concentrate on school work. Prior, I had only ever gotten one grade that wasn't at least an A-.
It strongly affected my grades in a negative way. There were grade average requirements to participate in nearly anything, forcing the school to pull me out of extra-curricular activities that were actually keeping me sane because they got me away from the hell that was my home life. It was a death-spiral for my academic situation, and it led me to hating school, thus killing my motivation even further. I plummeted, the only classes I regularly did better than a C on were music classes -- things I could absorb myself in. My GPA averaged less than 1.5.
I never did get my shit together, and eventually dropped out of high school, getting a GED instead. There was certainly a lot of blame to be directed at myself, for my own inability to pull myself together and do the work -- but the effect of my home life, and the resultant attitudes and bad habits were a detriment to me for years. I believe that to some degree, they still affect me today.
Had my school had a policy like this in place -- even a limited one, allowing a pass on a percentage of work -- I think I'd be in a better place today.