It's not inherently insolvable, it's just nearly impossible to solve because the alternative solutions tend to have "overhaul the global economy and human nature" as their prerequisite.

Pretty much all of humanity's tough problems, the ones we can't seem to make much progress on despite centuries or more of trying, are at their core coordination problems. We only really make progress on those when we can sidestep explicit coordination in some way. Every other kind of problem is usually amenable to technology, and we've solved most of them already, largely in the last 200 years.

Teacher shortages and increasing tuition costs say it practically is.