It's an open secret among educators that the brightest students learn to read at home. Early math is just practicing the same arithmetic over and over, because the logical skills for algebra just aren't present in a seven-year-old.
Art, music, and gym are actually really important in early childhood development, because they develop motor skills. Gym gives gross motor skills and major muscular development, and art and music give fine motor control. Penmanship is also important for developing fine motor control. For young children who can't yet engage in much logical reasoning, developing motor skills is appropriate and important. We tend to think in adult terms about what is the right thing for kids to learn, but small children are not adults and need to develop skills that adults take for granted.
Additionally, it's now understood that insufficient exposure to very bright light (say, sunlight) during key years is the main risk factor for nearsightedness. Cutting time outdoors during Winter, for lower-elementary kids (K-2), when school is monopolizing a good portion of daylight hours, is almost certain to increase rates of nearsightedness. Cutting recess in young grades hurts kids' eyes, permanently.
I disagree with algebra being too difficult for a 7 year old. You can learn geometric algebra at 7 with plastic blocks. It's a common way to teach math in Eastern Europe to young children afaik.
Excellent maths teachers can really bring a lot to the table with geometrical approach throughout the years.
Was occupational training ever the primary goal of public schooling -- even back in the days when most people went directly to the workforce afterwards?
You'll have to decide what the "primary" goal is, but there was certainly the sense in the past that a U.S. high school graduate would be suitable for most jobs, either blue collar (shop class used to be quite popular), white collar (academic classes, particularly English), or indeed housewife (home economy). No matter what, though, a mastery of the 3 Rs (reading, writing, and arithmetic) was considered essential to all of these (you have to know arithmetic to balance your checkbook, do taxes, measure for construction, etc.). High school wasn't necessarily a specialized occupational school, but there was an expectation you would be learning useful skills for your future.
That's what I'm getting at -- life skills are much more broad than occupational skills. Art, PE, health, sports, civics, etc. are taught in schools because they produce people with more well-rounded life skills, not because it produces better bankers or factory workers.
