No, for a couple of reasons.
1) It would encourage grade inflation excessively, and discourage students from going to the handful of schools that actively work to combat grade inflation. Since what an A is varies somewhat from school to school, pegging loans to GPA would be unfair. For instance, up until this semester, the University of Florida did not have minus grades, so a student who would earn a B- at another school would earn a B at UF. Meanwhile, Reed College in Portland routinely grades far more rigorously than other schools. So this creates a real and unfair disparity.
2) The vast bulk of student aid is loans. Even subsidized loans, if they are made through the federal direct lending program, are a roughly revenue neutral expenditure that tends towards profit, because they get paid back over time with interest. Simply put, the direct lending program is not a sufficient drain on our tax dollars to fret about.
3) Much as you may not like all the tragedies, the point of the student loan program is to help students from difficult economic circumstances, and educational success historically correlates with class and wealth. The students who are having trouble getting through are still ones who need help - because even with a college education that they did somewhat poorly at, they've still made major progress on what they and their children will be able to do with life. And that's one of the major points of the student loan program - to break cycles of poverty. A student who graduates with a C average has still gone a long ways towards breaking that cycle.
