I haven’t looked into the data carefully but this strikes me as implausible at first impression for a few reasons.

One is that cultures with highly structured time for kids like China do not have the same dramatic rises in mental illness, that I’m aware of. Two is that this seems to only apply to middle class or rich western kids (unsurprising for academic studies). You really think poor kids are spending too much time at piano lessons and not playing? No they have the opposite problem of too much lack of structure.

Overall this seems quite narrow minded to me. The only part of this that rings true is the cultural phenomenon of wanting to make feel everyone safe all the time, even from mere ideas and speech.