Maybe so, but on behalf of its client, the government? The court? Not on behalf of someone else who is not paying. Hard to imagine there was no other law firm that would take this job, and if not then that’s one more negative sign for validity of prosecution, right?
The judge’s selection is the conflict of interest, not the prosecution itself. Selecting a private firm that’s financially entangled with the aggrieved party to discharge the duties of the Department of Justice is extremely unusual and concerning.