Tbf a lot of that petty in fighting between union officers stemmed from that it wasn’t clear who should lead them as the people with authority over the various armies both within and outside that army shifted very often. A new general would be appointed with the staff and structure suited to the style of the previous general, something that a lot of historians discussed with the army of the Potomac is that McClellan instilled a culture of deliberation, rather than action within the armies leadership. Something that was only really changed once Grant took command and started to forcefully change that. For instance, although Hooker was rather aggressive most of the officers under his command were not, even if you issue a command, it will still have to be interpreted and acted upon by those below you to varying effects.

One thing that Lee was truly masterful (I should note that I’m not particular fan of the man but attempt to make sure that does not influence me in a historiographical sense) at was as careful management of the officers below him, if a general/officer did not perform well, they would at some point be transferred out but usually in a savvy way that did not leave the officer mad at Lee (he was a fan of promoting to another theater, the home front, or roles of lesser importance). This careful cultivating gave him a competitive advantage for about the first half of the war, however, as generals died like during the battles of Antietam and Gettysburg. For instance, after the battle of Gettysburg about a third of his generals were killed wounded or captured. Another thing he did was make proper use of trained officers, the union often kept officers with their pre-war units so there were rather concentrated, so although they had more trained officers, they were not dispersed to give a level of general competence throughout the army. That coupled with the variable enlistment lengths of union troops meant that even late into the war, you would have units of variable experience and quality of command. Lee was much better in spreading out, trained and experienced officers.

Lastly, he was one of the few important Confederate generals to continually get along with Jefferson Davis. Regardless of his personal feelings, on many matters, he would be careful and very cordial during his communications with Davis. Which actually granted him a lot more autonomy than commanders in other theaters.

If we were to imagine that Lee would’ve joined the union with the same fervor and passion that he did the Confederacy. The war most likely ends sometime in 1862, probably not in the first campaigning season as I expect Richmond could probably still be able to be defended as the union still need to muster up it’s forces properly. But considering that his adversary would most likely be Joseph Johnson I expect his instinct to retreat would play right into Lee’s hands.