Is there a point at which money would exchange hands before a formal suit is filed? If so, that is the stage I am surprised this didn't progress past.
The government, on the other hand, wants the publicity of having filed the suit to deter other companies from doing the same thing. I don't believe they frequently settle before filing a formal suit.
For a purely monetary resolution to avoid a lawsuit, yes, but in regulatory cases rather than disputes between private parties where such an outcome is often preferred to a lawsuit occurring, the government will often not be interested in such an outcome, and will instead prefer a consent decree with behavioral restrictions that have strong legal consequences. These have to have an actual active case, as they are are court orders to which both parties stipulate, not private agreements. (“Settlement” can cover either type of resolution.)
Let’s not normalize this as common occurrence.
There is absolutely zero reason to sue SpaceX except for political hitpoints.