I apologise, I should have been more specific in my language:
CJ (et al); I did read the question, I'm coming at it from a slightly different angle - I do appreciate it can be separated theoretically. When I say 'in practical terms', I mean flying an aeroplane. As in: "why care that in some circumstance lowering the flaps will decrease the induced drag, as far as the flying aeroplane goes, it still has more drag."
kenparry: I'll assume we got off on the wrong foot, and I guess I didn't explain myself well - I shall try to rectify..
An l/d curve is a composite of components of induced and parasite drag; and dominated by induced drag in on the left. You can draw 'curves' / graphs for either independantly. The L/d may be the derivative, but they are all very much related - for the l/d curve to change, the induced and / or parasite drag characteristics must have changed. So no it's not irrelevant.
I'm somewhat stumped that you consider that 1) and 2) are "correct, but irrelevant" - if you change the camber of the wing, you have a different wing. Even ignoring total drag and parasite drag (I'll try to word carefully here) you change it's induced drag characteristics, and furthermore, if you reduce the AOA, you put it in a different place on the induced drag plot. How is that not relevant? We all know that fat, cambered wings work better at low speed; flaps and slats allow us to approximate that fat cambered wing when we require.
I don't have numbers, but gut feel tells me that's got to be far more significant than spanwise flow and aspect ratio (else why can a PA28 fly slower with flaps - no change of aspect ratio there).. so I do consider spanwise flow/aspect ratio to be a 'red herring'. Maybe I should call it a second order effect
I'll also throw in a non-sequitur: how about negative flap? I know at least 1 light aircraft (flight design CTsw), and many gliders that use -ve flap settings in the cruise to fly faster (i.e. with less drag). My understanding again is that you're approximating a less cambered wing....
As for my knowledge aerodynamics - bit of an interest, long time glider pilot, and plouging my way through ATPL aerodynamic theory. Please feel free to prove me wrong - I'm happy to learn.