The system says that decisions involving monetary damages are made by juries, and decisions involving injunctive relief (ordering a company to do something or not do something) are made by judges. If you tack on a claim for monetary damages when your that’s just a tail wagging the dog, when your real focus is the injunctive relief, then that is gaming the system.
Or, to put it differently, the government invoked a damages claim that’s tangential to its case to get in front of a jury on a technicality. And Google invoked a different technicality to get out from a jury trial. Live by the sword die by the sword.
And whether any of this helps or hurts the government’s chances against Google is entirely irrelevant.