Problem was the Union was coming to him, trying to capture Richmond early and Lee was successful in defense. By 1863 Lee knew the South would soon be overwhelmed in the West and was staring to suffocate from the blockade. He was looking for a quick knockout by engaging the Army of the Potomac in the open where his ability to manouevre was unmatched. But he got drawn into a set piece battle with inferior lines and poor topography.
As it was he was able to hold out for 20 more months against overwhelming odds.
While everything you say is correct, I still think that Lee's campaign into the North helped turn northern opinion toward winning the war, where in the past many (quite probably the majority) of Northerners wanted to quit the war.