Any argument about emphasising grit hinges on the extent to which grit is actually teachable. As the original article states, the measurable effects of grit seem to be a near-equivalent of conscientiousness from the well studied 'big five' personality metrics, and (as far as I understand) the evidence shows that these traits are very stable over the years (conscientiousness slowly increases over age, but roughly equally even for people who have lead very different lives) and there are no known interventions that would reliably change them.

So an argument against an educational policy to emphasize grit is that, as far as we know, this will not actually increase grit in the students. Socializing children to view the world a certain way will have many effects, but not that.