Actually, I'm of the opinion that it is much worse than children simply working. Much of the child labor "sweat shop" concept is fabricated by the media.
Most children about 100 years ago simply worked for their parents - improving the family business or starting their own if they wanted to. They weren't all mining coal and being lashed by barbarians :)
Going to government schools is purely for indoctrination purposes at this point. Kids get out of high school or even college and suddenly realize they have very few real-world skills to fall back on.
No es bueno.
A state school provides you with a certain level of education not necessarily 'life skills' all though they do provide some of that to a degree, parents still play a part in children's education. Not sure what indoctrination is going on, there aren't many parents who can provide the resources a school can. This debate was whether some parents can provide a home based education and some certainly can provide that, many cannot.
I think life in general let a alone education is a million times better than a hundred years ago, though that view point may well depend on your status, obviously being rich would negate a lot of the problems of 100 years ago.
You only need to look at third world countries to see how hard life is for children and the work that they are forced to do, anyone who lives in a country with a state education should be very very thankful they don't have to live a life like that.
As far as the indoctrination topic goes, it's broad and worth looking into if you're interested.
In particular, it may be of interest just how the schooling system most of the world uses actually came into existence and what methods it employs to condition children's minds from a young age (like Pavlovian bells, etc.).
School teaches reading, writing, math and the scientific method... Then things get weird and children are forced to attend 12 years of it, minimum.
Life has not become much better than it was 100 years ago, though I'm interested to know why you feel it has.
I live in what you'd consider a third world country and have traveled to multiple others quite a bit. Life is clearly not what you're envisioning. :)