The way to deal with an impossible task was to chop it down into a number of merely very difficult tasks, and break each of them into a group of horribly hard tasks, and each of them into tricky jobs, and each of them..
(Terry Pratchett, Truckers. I read this when I was 6 years old but it always stuck with me.)
I do agree in general with what you are saying. But sometimes the trouble is that the subdivision (at least a good one) is hard to find.
Often enough it is that you don't understand the problem well enough. But sometimes you just can't seem to find the proper sub-problems. I have had this experience while doing research work.
(Terry Pratchett, Truckers. I read this when I was 6 years old but it always stuck with me.)