But to make hydrogen from electrolysis takes electricity. More than equivalent amount of hydrogen can generate even in a perfect system and even so, that still nets you 0 extra power.

Right now we're either missing a piece of this puzzle like a consumable catalyst, or this is simply the most effecient electrolysis process that can make 1kg hydrogen for < $1 of electricity.  Which is useless for powering anything.  It's cheaper to use the power directly than use it to make hydrogen (efficiency losses), then convert hydrogen back to electricity (with more losses) and then power the QRR.