Something was up, and Grant was trying to figure it out. Rosecrans had lost a battle, for sure. But the campaign in Tennessee was very successful as a whole.
@Rhea Cole posted that the initial reaction to the Chicka. battle was not that negative. But then Dana turned against Rosecrans, Thomas sent very alarming messages to Grant, and Garfield, who had political ambitions, seems to have been covering his behind and blaming Rosecrans.
And what did Grant write about the Tullahoma campaign? Overall it was well conducted. Grant wondered why there was not a better position prepared at Chattanooga, but there was a political explanation for that. Stanton was eclipsing Chase and Stanton preferred the neutral Thomas to the leaning Democratic Rosecrans. As you note, the attention shifted from possibly using Rosecrans as the alternative to Lincoln, towards Grant. And Grant wanted to win the war first before becoming political.