Just to explain my point: if a student has worse skills, whatever their reason is, they should have lower grades. That's what a grade is for.
Then, you may want to address the causes of such low grade.
What you don't want to do is penalize students for arbitrary reasons like deadlines, absence from school, et cetera.
This, I absolutely agree with. Last year I implemented a standards-based system. If you could prove to me you knew the material, you got the points. If you learned it later and proved to me you knew it then, your grade changed.
I did do homework grades (I was required to have one grade a week, and there's no way I could do enough continuous assessment), but it was solely participation and as long as you turned it in and tried (.i. didn't cheat), you got full credit.
Generally, I completely agree you don't want to penalize them for arbitrary reasons; to me, that includes homework. I had to do it, but as long as it was turned in eventually, and honestly attempted, they got full credit (it was like 10% the overall grade). To me, that's how it should be done.
Basically, I completely agree and didn't mean to seem as if I was disagreeing with you!