Took me a while, but I see what you're saying.
I still feel like there should be some disadvantage to throwing out half the wave. I mean for an ideal transformer, the current in the primary should be proportional to the current in the secondary, so the primary won't be sourcing any current for that half of the wave. However, I really doubt it's that simple for practical transformers. There will probably be some loss due to currents induced in the core for that half of the waveform. I am unsure of how significant this is.
What is this for, anyway? I can't think of many situations where ripple really doesn't matter that aren't totally trivial.
He is trying to make a switch mode (buck) that connects directly to mains.