What are school-aged people spending their precious time on?
Clash of Clans? Snapchat? Call of Duty? Binging Netflix? 4chan...ning? Smoking pot?
Maybe it's okay if we ask them to set aside a few hours to read a book or practice solving an equation or trying to do something that isn't immediately easy.
When I was a kid (at a Montessori school — no homework) I used my free time to learn programming, tinker with chemistry kits, and read while my public school friends toiled away at homework.
I guess that other kids could squander their free time in pointless gaming or Internet browsing, but there will be a few (or ALL of them, if you buy Maria Montessori's thoughts on the matter) that will use their free unstructured time to learn something interesting to them.
I was extremely lucky. My parents were both educators and very engaged. I hope to be the same to mine. But parents like this are all to often not part of a child's life.
Either way, I think your social position shows through in your reasoning. Being able to learn programming or tinker with chemistry kits at least to a point requires parents that encourage and/or support that kind of pastime. A lot of kids don't have that, and will simply not be exposed to the existence of programming and chemistry kits. (Books are generally more accessible, but there's also something to be said for parents encouraging and supporting reading – the people I know who like to read also have parents who like to read, and the people I know who don't like to read have parents who also never read, for what it's worth.)
Why are these any less beneficial than homework that's been demonstrated to have no benefit to the child? Until high school, there's literally no reason for the kid to be practicing math after school.
Maths is fun. That's a reason.
Maths is useful and some children can't pay attention in class. That's a reason too.
Analytical and creative thinking expands the mind, ergo maths.
Different kids have different needs. Busywork for homework certainly isn't useful except as a way solely to keep a child occupied.
The incredibly difficult trick is to find the right balance between relaxing and working, and to encourage an interest in valuable educational activities without forcing it.