Fair warning: none of the below will really be relevant to the thread, or it's offshoot topics. It's also a bit rambly. Feel free to read it if you like, but don't expect to gain anything insightful from it.
@Steve I had a whole long post I made last night using your chess example, explaining how even with chess you need both the training and experience, and it goes back and forth. In response to this line "Application can replace training."
Didn't send for some reason, but today I see that you clarified with the post starting with this "I'm not arguing against training nor foundational instruction. I'm arguing against training as a replacement for application."
What's funny is my post that didn't send was basically me explaining how that hybrid model you talked about is needed for chess, based on me teaching it.
Except not so much the hybrid model you described, but a different hybrid. Training first-then application (playing chess) for a while, then when a plateau is hit, diagnose and train, then go back to application (you dip a bit but then get past your plateau) and rinse and repeat. If you try to analyze each and every game afterwards, I've found (at least for the levels I taught to) then you end up a: spending too much time analyzing, not enough playing, and b: have too many things you're trying to focus on and no set clear goal with it. At higher levels (basically the level I grazed at my peak, nowhere near where I'm at now, or where I could teach to..), the b isn't really true since you're doing a lot more fine tuning.
Focusing on B: let's say I play a game and I'm doing well, but ultimately end up losing. I go back over the game, by myself, with my opponent, or with my coach. We realize that the key point in the game seemed to be a move my opponent made with his knight, that I could have stopped had I been paying more attention to his knight. So next game I play, I make sure that I don't forget about the knight (or even, I make sure that I'm paying attention to the individual potential of each piece). This may be too much for me to focus on and I completely fall apart. But let's assume I'm past the level where I can't focus on each individual piece. I do so, but now I'm not looking at the board state, and while he isn't able to make any moves that my coach or other spectators would label as brilliant, he ends up with control over the center by middlegame, and I end up losing. Okay, so now I've got to watch out for that. And I should also probably watch out for the individual pieces, but that seems like a lot to focus on, so let me just make sure I don't get caught off guard by the knight again. I'm playing a new game, watching for center-board control and the knights, and get caught in a key fork without realizing it. Oops. Maybe I need to do some chess tactic puzzles again. i do a bunch, I'm ready for any tactics, but again I get focused on that and lose control of the center without realizing it.
You can see how that could (and does) easily spiral out with me focusing on a bunch of different things, but never actually improving in any of them. Even with some wins splattered in, I'm still stuck where I am. The better option (again depending on your elo, really good players who just need to fine tune and can focus are past this part) would be to play 10-20 games seriously, record them (or have a coach watch) then review them afterwards to see if there are any themes. So if I was the player mentioned above, I might notice that my openings are weak and I need to focus more on control of the center. I do some practice games and learn some new opening variations to help me with that, and make sure I'm paying attention to it going forwards. I might miss some things I would have caught had I not been focusing on it, but eventually I win a lot more by doing that, and get to the next level of competition where I stall out and start losing more often than I'm winning. Now I go through again, review my last 10-20 games to see what changed, and see if there's some tactics I'm missing, did I start getting worse with control, am I not thinking far enough ahead, am I staying too far ahead, is my endgame failing, etc. And repeat the process.
I'm sure there's some relationship here to martial arts. If someone else wants to find it, feel free.