After decades of study I have concluded that Rosecrans was an example of the Peter Principle of rising to the level of incompetence. The engineer that made him such a brilliant organizer prevented him from becoming a brilliant combat commander. My conclusion is that an ideal division of labor would have been Rosecrans commanding the Department of the Cumberland & Thomas as commander of the army. They could have maintained their very productive partnership while each exercised his special gifts.
People who measure such things rate Rosecrans' IQ as the highest among CW generals... which is also the straight line for many jokes. He had an unhealthy habit of keeping his young staff up until 2:00am discussing Catholic theology. Under the stress of combat he would ride forward under fire. He would have the brains of staff members splattered onto his coat. This show of bravado deeply impressed the troops. Three cheers & a tiger greeted his appearance. Unfortunately, the stress caused him to shout nonsense orders in a jackhammer stutter to dumbfounded officers.
At Chickamauga a characteristically Rosecrans solution to his dashing around the battle space was implemented. The brilliant James Garfield had a War game-like board with unit counters on it. As reports came in, the pieces were moved accordingly. It was a preview of the aerial / satellite / drone real-time situational awareness of a modernHQ. It was a misplaced counter that gave Longstreet his opening.
Objectively, the compelling conclusion is that Rosecrans was not the man to break the siege & lead the advance to Atlanta. Dana's reports have been called a clinical report of the effects of stress & sleep deprivation. Grant's only criticism of the plans Rosecrans had for breaking the siege was that he had not implemented them.
In my judgement, Rosecrans was like a brilliant entrepreneur who had to step aside to let the enterprise be managed in a business like way.