I think that's actually a good idea, at least on a certain level. Children should be recompensed for all the labor they have to do for society. People argue that it's for their own benefit, but I think it's just as much the case that school is mandatory because the economy would suffer if it weren't, so in a sense they're slaves to the economy.
And clearly there's no need for them to know 90% of the stuff they have to memorize and they'll neither remember nor use it for the rest of their lives. They should be paid for the inconvenience of having to live by the rules set up by archaic and incompetent schoolboard decisions if nothing else.
School shouldn't even be mandatory, and because it's mandatory you can argue that even paying kids to go school is still not as good treatment as we give adults because at least adults have a *choice* of whether to do work for money. But I guess you could also argue that adults don't *really* have the choice anyway on a certain level. Even so, though, at least they get paid for what they have to do.
Also, paying children would at least make them feel like they're appreciated for doing all the work we make them do at those mental labor camps, as opposed to merely being underlings and tools of a society that puts demands on them just for existing, where everybody who comes out of the womb is automatically put into some kind of debt, where just to be loved, accepted and treated decently they have to sit still and quietly and perform 8 hours a day for us, always catching up to their homework, etc.
The realistic downsides to the idea, though, are 1) children, at least under a certain age, aren't old enouh to handle their own money, and many parents are going to take advantage of this and use the money for themselves, and 2) the public education system doesn't get funded enough already to even have decent teachers, the tax on the economy would be many times greater if all children were paid a decent wage for their labor.
But those are merely practical reasons not to, I wanted to make the argument that they should be 'on a certain level' anyway because I think having the stance that it's wrong or inappropriate for some reason to pay children to go to school on an emotional/value basis is pigheaded.