The trouble with discussing changing grades is that grades are so closely tied to the traditional school experience that it's nearly impossible to imagine any significant changes. Nearly all teachers had the same "points/grades/rules" systems growing up, they all did alright in such systems, and they feel it's only far they pass it on to students. While such systems work well for some students in some subjects, the vast majority of students come to school to "beat school". They come to collect points, an arbitrary token-economy commodity and go home. They have to sneak around, stocking up on easy homework points to survive damage they make take on exams. They have to make sure work is submitted on time so they don't lose their points as if they were rings in a Sonic the Hedgehog game. It's a fun little game...but it's not what school should be about, and it's an artificial construct people confuse with learning and rigor.
If you're going to change how grades work, you need to rethink what homework is, you need to rethink tests, you need to rethink "summative" assignments...you really need to do a paradigm shift on everything. It's not simply a matter of accepting late work or allowing students to redo assignments, it's about making students no longer addicted to point acquisition. Until that's understood, school will simply continue the way it always has. While it's not a terrible system, it's more about tradition than innovation in any sense of the word.