turning things in on time.

The point of education is to get them to understand concepts of your subject. It wouldn't make any sense, before the grading period is over, to refuse to take on an assignment where the student is proving they know the concept. Or, as a lot of teachers do, take off points for it being late. If they have mastered the concept they should get the grade that represents their understanding.

Again, the idea of standards based grading is not my invention. There are entire districts in Utah that are pushing towards this.

Here's one book if you're interested in it. Probably a bazillion YouTube videos out there too.