Back in 2011 in a different case involving the same agency, the same individual provided declarations in support of the agency position.
And lied under oath.
The court caught the lie, and the agency (and individual) admitted to lying to the court. The court was clearly livid, which is shown by their ruling and opinion - but the agency (and individual) faced no consequences. No contempt, no jail time, no investigation.
In federal civil cases the courts show federal agencies an extreme - and almost blind - level of "deference". They assume that everything the agency says is the truth, and that the agency is the subject matter expert in whatever issue is before the court. Showings of "bad faith" on the part of an agency almost always go nowhere, like the 2011 case above.
So taking a federal agency to court frequently does not result in a happy, just ending for the plaintiff. SpaceX taking the FAA to court would probably not turn out well, however the act of suing them and offering them settlement options etc. outside of court may be effective, and that may be their plan.