I went to a workshop with Diana Kotzegi, and part of the discussion was about tsumego. One question I had in particular was, "When I do tsumego problems, I know there is a solution, so it's a bit different than in a game. I feel like I can solve tsumego problems more accurately than 'in-game' problems for this reason.".
Her response was, "You need to do more tsumego problems".
I replied, "You don't understand. I do a lot of tsumego problems. The problem is that I don't recognize the problems in games - or I don't know if there is a solution in games.".
Her response was, "You don't understand. You need to do more go problems".

What I gathered from this was, it's true that go problems have a definite solution that we do not know exists in games; But if we do tsumego enough, we can get strong enough to see solutions on the board more easily.
Of course, I still agree with your new approach to tsumego; being thorough never hurts.