I would take it a little further back. Learning how to learn is the critical accomplishment. Human beings are not hardwired for this ability, and each of us learns how to aquire and integrate new relationships and associations in our own way.
It is tragic, but we must grasp that the true 'customers' of public education systems are not the children themselves, but the government. Unfortunately, many private institutions do their best to become better at the same methodologies. Thus, what should be the ultimate goal of education is not. All too often, traditional schools train ("condition", rather) children to focus on beating tests or outmaneuvering requirements, rather than acquiring knowledge itself. There is definitely survival value in both the 'beating' and 'outmaneuvering' strategies, but I would suggest that many of the ills we see in current society are strongly influenced if not directly caused by such emphasis.
Outside of the government's will in the matter, how one defines and rates intelligence and achievement in both abstract and survival senses has a great deal to do with the relative importance of the three concepts you ponder. The current U.S. President is a classic example of one whose survival traits have served him well, but his "achievements" raise serious questions in both net value and ethics axes. IMHO, the imprint of factory school mentality coupled with the rich kid syndrome are all over his behavior patterns.
There is value in any experience, even negative ones, and I do applaud the efforts of myriad unsung teachers within "the system" who do their best to spark understanding and creativity. It is indeed true that fundamental understandings must follow learning how to learn in order for AHA! to happen, and to me it is a miracle that so many children do grow up intelligent and learn to make their own contributions.
And, let me say, learn to be _humble_ contributors... Salud, blackstarr!
"There's more than one level to any answer."