The point I was making though is that the designers were intending the game to be played by people with no gaming experience. That's how the game is written to me. Since I'm not that, the advice doesn't really appeal as much.
To me, this experience would be far too structured and rely far to heavily on the DM being at the front and center of the game. Simply ignoring this bit of the game in favor of trusting that my players know what they're doing instead of having me have to judge every declaration means that we have a better experience.
5e is written from the point of view that it has to be played by 15 year olds who've never role played before. So, it gives a very structured approach - goal and method as you call it - which will work very well at nearly any table. There's nothing wrong with doing it this way. It certainly works. And, yes, it certainly would clear up misunderstandings if followed faithfully.
OTOH, it assumes that the group needs this level of structure and that narrative power over the game rests very squarely on the DM's shoulders. That the players have their area of control in the game and the DM has everything else. LIke I said, I have no problems with players declaring stuff to be true. In the earlier example of climbing the wall and using boxes, it would not bother me in the slightest for the player to declare that he climbed the wall because there were boxes among the bric a brac in the last room and that he stacked them up to climb over the wall. IOW, the boxes were never described prior to the player rolling a success.
Doesn't happen much, but, I have no problem with it. 5e does not grant much authorial control to the players by the rules. I prefer the players to have more authorial control in the game. I LOVE it when the players declare stuff to be true that I hadn't added in. Lots of "Yes , and" sort of improv stuff. Would not be something that would work in a group of new players as well, and would not work with the goal and method approach either since it's the success of a check that allows the player to declare things in the game.
I guess that is another central idea - for you, a check is called for when the players haven't found a way to do something without needing a check. For me, a check allows the players to author elements in the game that weren't there beforehand.