There's no sense in prescribing a change to "our grading system" without even referring to the content of the class that's being graded, based on the assumption that all the work a teacher gives out to students can be classified as "homework", which is for the purpose of practice, and "test", which is for the purpose of comprehensively measuring one's performance.
For example: If the teacher assigns a 10-page research paper or critical essay, most people wouldn't classify the paper as a "test", so under this schema it must be "homework". But I don't see how the skills that one could demonstrate by writing such a paper could also be demonstrated in an exam.
Actually, I would consider the large research projects to be the tests of that course. Besides, the English/lit/composition courses I've taken don't really give small daily or regularly assigned "homework" assignments anyway, so this plan wouldn't really apply to those.
What if the teacher feels that ten homework assignments can cover more breadth than two or three tests, and therefore can give a more accurate picture of the student's abilities? Would you also redefine those homework assignments as "tests"?
For example: If the teacher assigns a 10-page research paper or critical essay, most people wouldn't classify the paper as a "test", so under this schema it must be "homework". But I don't see how the skills that one could demonstrate by writing such a paper could also be demonstrated in an exam.