As far as I know, it was entirely by doing that we once learned. Dance and ritual then played a prominent role and later increasing sophistication of abstractions were woven into the tapestry, increasing our temporal and spacial vision as well as our ability to transmit information using token symbols just like pheromones are used as social currency in an ant colony.
We drifted from that integrated ritual-knowing approach with the introduction of writing. So "magic" was writing considered that scribes were their own class, and so powerful was knowing that it could now transcend generations.
With the advent of educational institutions born in medieval times in the west, we further emphasized the split between knowing and doing. The universities were primarily for the academics and guardians of the stories that bound us together. Rulers, priests and the like were the customers - it was part of the many eusocial differentiations of tasks that enabled us to increase our ability to effectively and reliably do additional things, including capture and record even more understanding more accurately at an increasingly accelerated rate.
My guess is our fascination with learning in the form of capturing things in a net of verbal abstractions came at the expense of forgetting how to do because of too much emphasis on, and belief in, the presumed magical power of verbal knowing. This, coupled with a downward look at the plebs who learned by apprenticeship was perhaps a mistake. Modern institutions still bear the hangover effects of this unfortunate social stratification. John Dewey was one of many who attempted to heal this divide. He tapped into the value of an immersive verbal, visual, tactile kinesthetic aspect of learning that is more suited to ingrain information in us beyond the abstract. To unlock the capacity to do. Modern education still appears to be largely lost in it's own little words to our detriment.
We are human beings, not human knowings. We become by doing, but I think this was somehow forgotten in modern pedagogy as a result of the flood of information, along with a loss of understanding how to foster our native curiosity. This was also exacerbated by the necessity to prime people for industry, which in essence tailored schools to ingrain an adherence to authority structures, timing to bells and obligations and to asphyxiate curiosity so people could function better as cogs in the industrial machine.
There are some things that are being done to make learning more immersive. The Anatomage Table looks promising as a step, but I agree with you this could be taken much further. https://www.youtube.com/watch?v=6FFd6VWIPrE
I also think Sugata Mitra is on to something with immersion. If you have not heard his TED talk, I highly recommend it.