Okay, I'll bite.
Yes. In the same way that a cure for Polio emerged: someone will have to invent it.
Oh, wait, "system?"
You mean like organized and managed by governments? Then no. Governments really have no desire or use for well-educated, knowledgeable, wise, insightful people.
On the other hand, if you mean "system of learning" that can be installed in schools so that actual learning happens and understanding is achieved, then yes.
There are systems of learning that work, some better than others. I have my favorite; I'm sure others have theirs.
Unhappily, governments mostly see this as dangerous: people who actually understand are harder to brainwash and control. Consequently, left up to the gummint, it will actively be prevented.
It's worse than that. One of the reasons for the dramatic drop in effectiveness of the U.S. public school system since the mid-sixties is the de-emphasis on academics and the emphasis on social engineering mandates from policymakers. Many people have hopes that charter schools will end up causing improvement in the traditional public school system through competition. I think charter schools will have a transitory benefit by getting parents to think in terms of education options that are better for their children. But in the long run they are doomed because they are funded by the same policymakers. With their innovative teaching techniques, they will just become very efficient engines for social engineering mandates. There still won't be the time to actually teach academics and to teach the students how to think.
I suppose criticism of institutions of government and educational institutions can be expected, but what can we say about how Education Occurs? Are we the mindless, manipulated victims of a system aimed at making us more and more vulnerable? I think not. There are far to many resources which can provide information and the power that that information brings. If we can muster the effort required, we can be the possessors of a high level of education and enlightenment. But we must first have a curious desire to KnowAbout?.
It is usually the case that education takes place when curiosity is awakened. To assume that people are educated only in schools, and by institutions is to miss the part of the iceberg that is under water. Education of the individual takes place regardless of institutions. I would even go so far as to say that knowledge that is applied by the individual is integrated into one's personality by personal choices. If you want to learn, there are many vehicles which will take you there, only one of which is institutionalized schools. To expect to learn without personal effort is like sitting down at a table full of food, and expecting someone else to feed you. So once we learn that education is good for us, we begin to crave more of it.
The web can be a system of education: