1. To succeed you need something to model, and some way to feedback into the system when the results are those which you didn't want. Lots could be written on this process.
2. I can write a chess program (with a lot of effort) that could as good as me or better knowing rules to find tactics, opening variations, how to play certain endings... As soon as you give it something which isn't a clear case of one of those inputs, at best it can play a random move or based on some heuristic (which is what happened with these kids, not to mention they'll get bored and frustrated). The magic of a plan comes from not knowing fixed rules, but some feeling of having seen something before (which is also how Alpha Zero and the others work). Rules often can take us in the wrong direction, and when the feeling and the rules diverge, calculation or other judgement is needed). Thus studying games of those better than you - just playing your peers is a slow trial and error process. However there is still the missing piece of how to study, which hopefully will be a future article.
3. Finally without a good coach you have the problem about getting good feedback and being directed on the right track. See Why do you Lose post for some ideas there. I'll try to write a follow up to my investigation and how I aim to correct the issues when I get some time. How to learn from your mistakes is a good basis for another article. Analyse your games with / without a computer is pretty vague, but that's often as much detail given..
Listening in his interviews and streams I doubt Nakamura studied the classics. I think he didn`t know who was Smyslov. :(
When trained by Kasparov Naka said they diascussed a lot about engine variations. I think Naka best coach is Stockfish.
You were lucky to have a chess fan in your father. Carlsens father saw the burning desire of his little kid and instead of taking him to a chess school he hired one of the few GMs in Norway, Simen Agdstein. The rest we know, Agdstein amazed about the kids talent, his father taking him out of school and buying a van were they could travel across europe searching tournament aqnd opponents.