That would be fine, except for the fact that some of the people in charge of setting curricula don't want that kind of education to happen. Where they are in favour of that, there are others working to get on school boards and other positions of power to explicitly battle such education.
I don't know much about the rest of the world, but Canada and USA both have increasingly powerful factions trying to take over school administration at all levels.
Here in Saskatchewan, we even have a Minister of Education who is deeply involved with the creation and support of "Christian Academy" schools that are little more than bible study groups.
Off the top of my head, I can't think of any advance that didn't at some point depend on people just dicking around to see what they could see.
"What happens if we spin this stick really really fast against this other stick?"
"Cool! What happens if we put some dried moss around it?"
"That's nuts, man! Hey, I wonder what happens if we toss some of our leftovers in there?"
"C'mon over here, guys. You gotta taste this!"
At worst, a project like this keeps a lot of curious people in one place where we can make sure they don't cause harm with their explorations. At best, whole new industries are founded. Never forget that modern electronics would never have existed without Einstein and Bohr arguing over the behaviour of subatomic particles.
Say the actual construction cost is $100 billion over 10 years and operational costs are $1 billion a year. Compared to all the stupid and useless stuff we already spend money on, that's little more than pocket lint. We could extract that much from the spending of one military alliance and it would look like a rounding error. Hell, we could add one cent to the price of each litre of soft drinks, alcoholic beverages, and bottled water and have money left over.