[dmurray]

> In particular, in that variant it would be so easy: just let the first move be duck only!

I don't see why that would make a significant theoretical difference. Black plays first and moves the duck, he can block either e4 or d4 (or something offbeat like g6 if what he wants is to get a Modern Defence at all costs) but not the other one. I suppose there's a practical difference where White couldn't specialise in e4- or d4- openings, and Black gets to choose which to face depending on the opponent.

(And in any case, as above, I disagree with the thesis that the imbalance should be "fixed").