I expect the biggest problem is that giving teachers flexibility to give class credit for random projects outside the syllabus would quickly become the much eas

I expect the biggest problem is that giving teachers flexibility to give class credit for random projects outside the syllabus would quickly become the much easier route to passing the class. The more restrictions you put on the project, the more you take away from the students interest ("sorry, carbon nanotubes is not one of the allowable project materials") and the more likely you'll need to demand unreasonable beaucracy ("the published paper doesn't include the teachers name as lead author so it doesn't count. write it up again without plagerising"). Plus there are some benefits of a syllabus, such as making sure that fundamental knowledge is taught. If you (as a student) missed algebra because you were doing your investigation into fractals, you're going to find calculus much more difficult than you would otherwise.