Privatization of military functions was a key reason for the downfall of the Roman Republic. Troops became loyal to generals, not to the Republic herself, as the general became the paymaster/generator of funds. The echos are getting louder.
These mercenaries are closer to Crassus hiring legions to fight a foreign war moreso than Caesar or Sulla marching on Rome. American firepower is predominantly state owned and loyal to its civilian leadership. These mercenaries are a liability because they make America look bad, not because they pose even an intermediate threat to American military power.
It's not clear to me why Roman Empire would be relevant in this case. Society, economy, politics, military, culture, technology, wars, the life of soldiers... a lot of things were different back then.
There are always lessons in history, even accounting for the differences between an agrarian and digital society. Private militaries have proven to be rather fickle when it comes to rights v. might.