What if General Robert E Lee was sent to fight in Tennessee? Say, after his loss at Gettysburg? How would he affect things and how would things change in Virginia?
Longstreet maybe? He was the CSA's most senior Lt Gen and Lee's second in command of the Army of Northern Virginia. Other options may be Joseph E. Johnston or P.G.T. Beauregard.And then you have the question of who takes over the Army of Northern Virginia and whether this leads to more political interference by Davis in its operations and command structure. It's possible the CSA's war efforts are actually less successful under these conditions.
These scenarios keep coming up because Davis never solved the problem of who was to command the Army of Tennessee, the "other" Confederate field army, after A.S. Johnston's death. Lee was the only Confederate army commander who was both a success at the military operations and had the confidence of Davis. The problem is that there is only one Lee, so that moving Lee to the Army of Tennessee now means that you have a command problem to solve with the Army of Northern Virginia. And the Army of Northern Virginia was the more important of the two, and in the theater Lee was more familiar with and Lee was more familiar with working with that army.
So using Lee anywhere other than where he was used IOTL was sub-optimal, and for that reason I have a problem with Civil War wargames where that is a good move (at a minimum the rules should not allow that). Even if you give Lee overall command of all Confederate armies earlier than in 1865, it doesn't change much because he still stays with the ANV as the de facto if not de jure commander, what you really wind up gaining, which admittedly is not nothing and Lee is a buffer between Davis and Beauregard and JE Johnston, both of whom Lee had higher opinions of than did Davis.
The good news for the CSA is that the two Army of Tennessee commanders they used most often, Bragg and Hood, should both have been excluded from consideration off the bat on health grounds, Bragg due to mental Health and Hood due to physical injuries. People in the mid-nineteenth century wouldn't be expected to understand that and Bragg at least looked good on paper, and neither were total disasters. However, it should be easy to at least improve on Bragg and Hood just by moving in someone in decent mental and physical health. JE Johnston, the obvious alternative especially since his own tenure was quite credible, was unavailable in 1862 due to his own injuries. There were only two Confederate field armies, so we can't be sure how well any of the other generals would have done in army command, excepting Beauregard's brief tenure at what became the Army of Tennessee.
The most obvious POD for sending Lee West is as a butterfly to JE Johnston not getting wounded at Seven Pines. Even better, have the attack succeed and JE Johnston saves Richmond in 1862, no he does not retreat and abandon the city. Davis' confidence in JE Johnston improves and he remains in command of the Virginia army. Instead of replacing Beauregard with Bragg in the West, he sends Lee to that command. Lee seems to have been kept on the shelf anyway before Seven Pines in case a command change was needed at one of the two armies. It happened that the Eastern army vacancy came up first/ was more urgently needed to be filled and Lee was better suited for the eastern army anyway.
Now if done this way, the CSA probably does get more out of it than the iOTL arrangement. Virginia is a more suitable theater for the sort of holding operation and delaying tactics that JE Johnston was likely to do. The West was too large for one field army to cover, so the tactics needed was to hit one of the federal armies hard with a counter-attack, which in fact Bragg kept trying to do and even JE Johnston tried to do at least once. But Lee was more likely to pull this off and would have had more clout to get the subordinates he needed to pull this off. But this is offset by Lee going to a smaller command and army, and one he is less familiar with, so unless there are substantial butterflies it is far from a war winning move, and could lose the more more quickly if the eastern commander turns out to be not competent.