There are a lot of practical skills that are not a part of traditional notions of school but that arguably could or should be. Basic financial skills are usually included in such a list, as well as anything to do with car, home, and work-life maintenance.
Why schools provide so little practical preparation is something of an interesting mystery, opening the door (for those who are ready) to a deeper conversation on the purposes of schooling. But that's a topic for another day.
More apropos to Pauling's quote, why is it that so many important thinking skills and strategies are not taught?
If having good ideas comes in part from having lots of ideas (and it's surely a very significant factor), why do we rarely discuss the collecting, curating, care and feeding, testing, and ultimate filtering of ideas? Do we ourselves have a system for keeping track of ideas? A journal, perhaps, or a folder on your phone for audio notes, or a way to use Evernote or Trello or some other electronic tool?
I certainly do, and those methods are some of the most significant elements of my intellectual/work life. How would we teach these methods?
Or, similarly, what about the mental tools that allow us to understand and take advantage of how our ideas change and deepen over time, sometimes taking years to come to fruition--do we have conscious strategies for allowing time to work on our thinking? I would guess that most of us do, but maybe have never articulated them even to ourselves, much less tried to pass them along to others.
What about learning the value of true diversity? These would be the skills of listening to and truly considering perspectives different than our own?
Or the crucial importance of developing meta-cognitive awareness, including the abilities to manage our own emotions and responses, to not get trapped by basic forms of propaganda and logical fallacies, and how to avoid the dangers of group-think?
You're likely to have thought of other skills I haven't mentioned.
In some ways, the greatest riches of intellectual life lie undiscovered and untapped by our current definitions of education, unless one is lucky enough to find a real mentor or is encouraged to read great books (the measure of which in many ways is their ability to bring to life this kind of thinking). College used to be the place where much of this intellectual work was discovered, yet now seems often as barren of this focus as secondary education usually is.
If schools are for developing thinking skills, perhaps we might measure how we are doing by how we answer the questions above.