What is the point of school?
That's a big question, it's tied to everyone who has started a school, how a particular schools is chartered, what its hidden goals may be, what the educators think it is, what the public as a whole believes, parents, and students.
I'm looking the reason we send "children" to schools at all.
I send my child to school because she's with children her age in a controlled environment that is conducive to learning things that she'll need to know to compete in our marketplace. It's supplemented at home and in outside of school learning activities. We specifically chose her school and teacher such that it meets with our expectations.
Is it to give a basic understanding of life and the world around us?
Partially, sure. All knowledge gives us greater understanding of the world around us...by definition.
Social exposure. Not sure what you mean by indoctrination. If interacting with others is indoctrination I suppose, otherwise I consider it a life skill, and more fun than playing with dolls (so I hear!).
Prepare the child for work in the 'Real World'?
Sure, but I expect it will mostly be fundamentals they learn in school. The *real world* education is typically not going to be found in a traditional school based on my understanding of schools. That will largely come from her parents, because schools are probably 30 years behind where they should be if they were not so detached from consumers.
Or just a goverment babysitter?
To a degree, but government doesn't make the babysitting role bad, if it were private we'd still use private schools as a baby sitter to a degree as well. Nothing wrong with this. Personally having a child I intentionally want my child in a school or school-like environment. I don't know how home schoolers do it, but I think my child would kill us if she had to sit all day every day with us lecturing her, without other kids to interact with, a teacher who is perceived differently than a the parent doing the educating, etc. I think we'd be doing it wrong if we did not send her to school. But for us we are picky about the school and what she learns.
Is the way we are doing it now working?
Is what our family is doing working for us? Yes. But it's terribly inefficient and expensive currently, so from that perspective no its not working for us, but our daughter won't really have to absorb that part.
If not What would work better?
Public education reform to look like every other successful industry that changes with the times, reacts to consumer feedback, has competitive costs, etc