Only Do Math Homework
Following an identification strategy that allows us to largely eliminate unobserved student and teacher traits, we examine the effect of homework on math, science, English and history test scores for eighth grade students in the United States. Noting that failure to control for these effects yields selection biases on the estimated effect of homework, we find that math homework has a large and statistically meaningful effect on math test scores throughout our sample. However, additional homework in science, English and history are shown to have little to no impact on their respective test scores. (more)
So does anyone think that once this result becomes better know, they’ll stop assigning all but math homework? Me neither. Yes, maybe homework helps kids to learn things that their tests do not test. But more likely, homework functions to get kids used to doing a lot of work, in preparation for their future industry era jobs. Learning seems secondary.
Most teachers I know don't want to assign homework, but get grief from parents if they don't. I also know teachers who've been accused of not working for not assigning homework. Often, the only time my students ever had homework is because they mucked about in class and didn't finish it then.
Also homework takes on the role of seat work. Seat work has been frowned upon for about a decade now. The populous want me pestering/lecturing/engaging my students (a.k.a.working) at all times. Most people think the time teachers spend sitting in class watching students work is teachers being lazy. Therefore, teachers don't do that, and students have to do all that essay writing, reading, and quiet thinking at home. (For the record letting students work quietly is mind numbing and the only part of my job that is worse is the never ending marking and meetings)
It's often more social pressures in the educational/parental environment that result in homework. Most teaching courses in my country don't recommend or are against homework. Most teachers (that I know) are against homework, even math homework.
"Also, developing homework assignments in non-math subjects which actually are educational is clearly hard. (Otherwise, such homework would already exist...unless you think they suppress it intentionally.)"
Since, as Robin points out, education systems are not exactly jumping on this sort of research, my guess is they haven't tried very much.