Are you suggesting that Rosenstein stay in his position?
I won't presume to speak for anyone else, but in answer to the OP's question: YES! He should stay (for now).
Firing Rosenstein isn't going to stop Mueller, in fact it will further enable him, making him untouchable.
If someone has to be fired it should be Sessions. Who, Trump has called out many times as ineffective.
OK, the FBI has a very strange org chant: everyone in the FBI reports to the Deputy Director. The only direct report of the Director (Sessions) is Rosenstein. The Deputy is far more important than the Director in day-to-day stuff.
If Mueller is fired Rosenstein becomes acting Deputy Director. Trump then replaces the vacant Deputy Director slot with his guy.
Now Rosenstein is pretty isolated. He's got Trump above him and Trump's guy below him running the entire DOJ.
At some point if Trump does fire Rosenstein Trump's new Deputy becomes Acting AG, which effectively prevents Democratic approval drama. He can stay as "acting" forever, if Trump lets him.
If Mueller Sessions is fired Rosenstein becomes acting Deputy Director. Trump then replaces the vacant Deputy Director slot with his guy.
Fire all three of them(rosenstein, sessions, and mueller) and start building gallows.
You’re confusing the DOJ and the FBI. Wray is the director of the FBI and David Bowdich is the deputy director.
Sessions is Attorney General and Rosenstein is Deputy AG. However in the DOJ org chart, the AG has no direct reports, everyone reports to the Deputy who then reports to the AG.