Even in America, I had that experience. Shows often show things that are outdated, only introduced in middle or high school, or that only exist in some regions.
We didn't get lockers until middle school, and in not middle and high school they were tiny with only enough space for a few books, not the ones big enough for bullies to stuff people into in shows. We didn't use the ABCDF system in elementary school. Our desks did have a little storage compartment, but they didn't open from the top. It was just kind of like a drawer under the surface but without the drawer.
I think the showmakers tended to conflate their memories of Elementary, Middle, and High School all together. That's why you also see elementary school students learning stuff that's way too advanced for the age they're supposed to be.
Yes, because the centaur can carry the good archer for double the firepower.