Should society eliminate schools?
The question is too vague as it's stated, but I think society should eliminate schools in their present form. This is a rather worthless statement though, at least unless it's fleshed out by a reasonably detailed description of what that alternative world would look like.
I think it would be a substantial win to at least cut down the years of schooling on the margin and replace them with work and/or apprenticeships whenever possible. An uncontroversial example: the fact that physicians and lawyers in the US have to complete a whole separate undergraduate degree before going to medical school or law school seems like a colossal waste of time and resources, and many civilized places in the world get by just fine without this extension.
So on the margin, I think it's good to move in the direction of "eliminating schools". Whether you want to go all the way and what happens if you do is more complicated, though I think there are definitely more promising alternative systems that would qualify. These are more speculative and only of theoretical interest given where we currently are as a society, though.
Should we have more compulsory schooling?
On the margin, I don't see how more compulsory schooling would help with anything useful, and the costs are significant, even aside from the moral concerns with forcing children to go to school et cetera. So the answer here looks fairly overdetermined to be "no" unless marginal years of schooling are shown to have substantial benefits.
Should you send your kids to school?
Depends on the situation. Do the kids want to go to school? Do you think careers that would be the best fit for them require one to go through some formal accreditation process that involves schooling? How feasible it is for you to arrange an alternative to going to school for purposes that are relevant, and what are the costs of not participating in the existing system?
I would put significant weight on the preference of the kids in question here, and I can easily imagine that some of them want to go to school and others don't. A "one size fits all" policy seems inappropriate here.
Should you prefer to hire job candidates who have received more schooling, beyond school's correlation with the g factor?
There are other reasons to prefer such candidates, but it depends on exactly which job you're hiring for. People who are "competent" despite not going to school right now are all highly unusual people in various ways, and they might generally be unusual in a way that makes them poor fits for the specific job you have in mind. So in that case going to school would be a valuable signal above and beyond the correlation with g.
Should we consider the spread of education requirements to be a form of class war by the better-educated against the worse-educated which must be opposed for the sake of the worse-educated and the future of society?
Probably not. I don't see what reason there is to invent such an explanation for the phenomenon of schooling, or what predictive power or utility it would have.
I find it more productive to view schooling and its shortcomings (as many other things) as coordination failures and problems imposed by scarcity than any kind of "class war" by some group against another. Useful thinking about these questions should contend with the coordination issues surrounding signaling etc. and the substantial opportunity cost of having high-quality teachers in too many classrooms.