There once was such a world. It was the world of the eighteenth-century European aristocracy.
Consider, if you will, the proportion of the education of an eighteenth century European aristocrat that was devoted to activities that fostered empathy - fencing, dancing, horseback riding, hunting, conversation, music, art appreciation, and travel - and how little was devoted to things that were purely academic. Moreover, the approach to academic subjects was different, with an emphasis on familiarity with a canon rather than the ability to do well on examinations.
As we are discussing this question on the "after 1900" forum, I will place the point of departure in 1914, when the German decision to attack Russia while defending against France led to the defeat of Tsarist Russia, the collapse of the Third Republic, and the survival of Austria-Hungary. In the aftermath of this grand event, a group of European intellectuals made three observations. The first was the extraordinarily high cost of modern battle and, in particular, its power to deprive society of its best young men. The second was the need to prevent the "Germanization" of Europe. The third was the attractiveness of the Austro-Hungarian approach to life, with its emphasis on courtesy, tradition, beauty, and the enjoyment of legitimate pleasure.
After much discussion, these thinkers came to the conclusion that the key to limiting German influence was to promote a powerful alternative to the excruciatingly academic approach to elite education that had become such an important part of German culture. This, they believed, was a revival of the eighteenth century approach to education, one that relied on governesses, private tutors, and "masters" (fencing, dancing, riding, drawing etc) rather than professors and examinations.
This "empathetic" approach to education offered the added benefit of inherent exclusivity. That is, the fact that it was expensive to provide such an education prevented the sort of thing so often seen in largely academic systems of education, in which clever young people from modest backgrounds regularly beat scions of the upper classes at their own game. In other words, the replacement of the (British) public school model with a revival of eighteenth-century education would make it much harder for "grammar school lads" to beat gentlemen at their own game.