There are two sorts of difficult puzzles:
First, the ones with lots of calculation, and deep variations.
Second, the ones which could have been easy if you simply had spoted it.
The 2708 CT Blitz rated (your example) is a puzzle of the second category: the relativelz easy ones that for some strange reason almost nobody gets correct.
I would love to have some puzzles sorted into these two categories.
I could imagine it is worth to study the character of the "easy" puzzles, that are very difficult.
90% of the 2200 - 2300 rated puzzles at CT fall in the category "easy" imo.
This weekend I worked out about 30 of them while looking what is going on in my mind. I noticed that the patterns are well known enough usually, but I fail to concoct a flawless logical reasoning. That is strange, since I usually score very high in tests of logical reasoning.
This means that the ability is there in principle, but something is lacking.
Look at the following diagram of a 2299 rated problem
You can find it here.
White to move.
The patterns are simple enough, the problem isn't very deep, yet it is easy to go astray due to lousy reasoning. What I found is that there are basic elements of logical reasoning too. But to concoct them yourself on the fly is an error prone business. If you write those elements of logical reasoning down though, you recognize after a few problems that the same kind of reasoning happens over and over again. What I'm trying to say is that it should be possible to automate the uprise of the basic elements of reasoning so that they come to mind without effort. Just like patterns do. In that way you can add intelligence to the solution of a problem and yet make maximum use of the automated semi intelligent elements of reasoning. (Still somebody there?)
The dog above performs a semi intelligent action.