Another way to think about Mark 1's post is this:
You need to accelerate a mass of air backwards to generate a force to move your engine forwards.
You can accelerate a small amount of air by a lot, or a large amount of air by a little to get the same force. But the fuel flow is related to the kinetic energy of the air-- the amount of air times how much we accelerate it squared. So let's do a small acceleration on a big amount of air.
That's why big props are more efficient. Big props spinning fast get higher tip drag, for sure, but that's tangential drag (harder on the engines) and not axial drag (slower airplane), which is what octas8 just said, too.
If you have a big, flat propeller that's not spinning in flight, sure-- you'll have a lot of axial drag. But I don't think that's terribly relevant to the dynamics of the prop in flight.