It might strengthen the US's case that there is an antitrust problem, but if the remedies don't actually fix the problem but instead make things worse, it certainly undercuts their case for the remedy.
This only ends with Mozilla getting less money since without Google bidding the value of the placement goes down.
Just as the Microsoft antitrust case was never about whether it was legal to bundle a browser with an OS, but whether Microsoft's particular act of doing so was illegally leveraging a monopoly in the desktop OS market into other markets, the Google case isn't about whether its legal to pay to set a search engine as a default but whether by doing so Google was illegally protecting an existing search monopoly.
You can't just ignore the relevance of the market power premise of antitrust cases to which it is central and pretend they are about the actions without regard to market power.