I'd argue that is a big part of the point I am making. If you take too big of a bite the time it takes to build it optimally goes up in an NP manor. If the bites are the right size then it balances the time/resources you have compared to all the other bites you make to get a locally optimal answer given all resource constraints. Long story short, cutting a problem into manageable pieces is a solid strategy. I will add one thing though, and that is that most people think they have cut things into manageable pieces but in reality they have left them too intertwined and they aren't really independent pieces. For divide and conquer to actually work requires that the pieces have clearly defined, and very limited, communication.