The article raises some good points, but I also have some strong reservations.
Take the examples, for instance. The author puts a lot of stock in what Nabokov and Da Vinci did themselves in their youth and calls this 'agency'. But at the same time, conveniently or inadvertently, the author doesn't expand and look at the broader picture in which those individuals lived and how that determined their lives.
Nabokov was born to a very wealthy and prominent Russian family with ties to Russian high nobility. He had access to a breadth of networks, resources and means to develop into the person he became. Without disparaging the his talent as a writer, it's equally important to acknowledge that his early life wasn't burdened by poverty, bad health, illness, instability and so on. Nabokov himself even described his childhood as "perfect" and "cosmopolitan".
Da Vinci, on the other hand, was born out of wedlock outside Florence to a lower class family. The historical record regarding his life before his arrival Florence is fragmentary at best. What can be deduced is that his early childhood must have been tenuous and turbulent, living in different homes with different family members (grandparents, uncles, mother). His own parents went on to live separate lives as well. We do know that he only received very basic education - reading and writing vernacular - as a child.
Da Vinci's life was determined by a stroke of chance. At age 14, his family moved to Florence and he was lucky enough to end up a studio boy at Verrocchio. He became an apprentice at 17 and received 7 more years of training. Even so, at the same time, it's clear that his family wasn't wealthy and so he might as well have ended up in a very different place at the time e.g. working as a clerk for a budding bank, notary, or even an industry like a tannery.
It should be clear that 'agency' only counts for so much. Neither Nabokov or Da Vinci are exceptional as millions of others also engage in poetry or drawing in early childhood. External circumstances such as birth and chance are just as determining. From a historical perspective, the author can be perceived as falling into the traps of hindsight bias and survivorship bias in that regard.
Even so, the article does make a valid criticsm regarding education systems. Transferring knowledge through rote exercising and standardized testing serves a purpose. The upshot is that it allows for scaling basic education towards millions, which is no small feat to accomplish. The downside is that doing so ignores the needs, traits, ambitions, strengths and weaknesses of individuals.
Modern educations systems were first formed during the 19th century Industrial Revolution, and further grew during the 20th century when humanity experience profound growth, economical and technological advancements. It should be noted that there never was a unified vision on education, and the argument in the article isn't new by any means.
During the early 20th century, incumbent education was heavily criticized by emancipatory movements. Helen Parkhurst, Maria Montessori, and John Dewey were influential educational thinkers who addressed some of the issues touched upon by the author as they laid the groundworks for an educational framework called the Dalton Plan.
https://en.wikipedia.org/wiki/Dalton_Plan
At the same time, Célestin Freinet is another influential educational thinker who created the Freinet system, addressing the same criticisms, which is widely adopted throughout the world:
https://en.wikipedia.org/wiki/C%C3%A9lestin_Freinet
https://en.wikipedia.org/wiki/Freinet_Modern_School_Movement
Finally, the article betrays a fallacy hidden in it's subtitle: The world is a very malleable place. To an extent, the world is malleable. But one only controls one's actions, less so the outcomes. Human life is complex, unpredictable and capricious. The impact of some decisions can sometimes only be gauged several decades into the future.
While we consider Da Vinci a succesful individual, a young Leonardo would quite likely have been just as anxious about what what the long future held in store for him as the next young person today. In that regard, it might come across as ironic that Vasari has recorded Leonardo lamenting in his deathbed, aged 67, that "he had offended against God and men by failing to practice his art as he should have done."
In the end, it's not unwarranted to consider the author's question "Do children today have useful childhoods?" carrying a due amount of presumptuousness as well. While lamenting how society tends to shoehorn millions into a corset of conformance towards norms and values, it would be quite ironical to fall into the same trap and subject younger generations to different, yet at the same time equally high, expectations and standards maximally living up to purported 'agency' given for the sake of 'agency'.