Like economics, education is Trek is something that works great until subjected to scrutiny. Neuroscience does suggest some ways that learning could be improved, but often what people who try to shape educational policy are looking for shortcuts that only work for a small number of kids"grit" comes to mind. OTOH, kids specializing at early ages makes some sense. Young kids might just be working with objects oriented science tools that let's them play with the concepts of quantum physics without needing to go into depth. At age 12, kids are already able to start specializing in topics related to programming, hacking, Robotics, aviation, etc. If they could clear away their other subjects, they might rival adults in terms of knowledge and ability by 17.
Of course, they lose a lot of non-specialty knowledge, or anything that is not central to their job would get neurally pruned away. I think that this is unwittingly shown in Trek. Everyone took temporal mechanics at the academy, but no one remembers those lessons. Knowledge of biology is limited to a few, and real medical care still relies upon a doctor. Musicianship is limited--I think only Spock, Riker, Sisko, and Kim learned it as a lifelong skill, and only Picard picked up an instrument as an adult (no, I don't buy that O'Brien plays cello). There don't seem to be many readers. And when it come to perspectives on civics and political process, crewmembers often need thr captain's perspective in order to come to appropriate decisions.
I think that a lot of the expertise we see is shown to serve thr drama. When Kira needs to do something to the warp core, we should understand that she has people helping her or, in line with what a lot of technical people do, they open the manual, playback or troubleshooting guide and start working down the checklist. The crew probably spends more time looking up procedures than what is shown in order to keep the pace of the plot moving forward.
