I can't speak for them, but I can tell you that would add an enormous amount of overhead and risk for the lawyers involved. If you assign them your copyrights, their job is just to find GPL violations from the pool of projects they have the rights to and then initiate an action in court, which they do for a living. Without assignment, they can no longer proactively investigate with any reasonable chance of success, and they have to find a violation that's in a goldilocks zone; they need a GPL author whose rights have been violated and is willing to make a long term commitment to actively participating in litigation, that they know will communicate with them as needed, and who won't suddenly move to Nepal or be convinced by people online that they need to drop the suit or something.

If the developer owns the code: The violator may offer to make things right by releasing the code. The developer may choose to accept this offer, leaving the lawyer with little.

If the lawyer owns the code: The violator's offer to simply release the code is refused by the lawyers, who go for the jugular and try to bleed the violating company for as much money as they can.