Perhaps you are right, but Lee was an aggressive military commander. Lee obviosly was not going to sit still in northern Virginia and be crushed by a larger force. Sooner or later you have to assume even the most poorly-led force is going to get a clue (or get lucky). I guess what I'm saying is that Lee-being-Lee, he could do nothing else.
This is why Jefferson Davis comes in for so much criticism. It was his "military genius" that selected the major field commanders for the Confederacy. Lee was brilliant in raising the siege of Richmond in the 7 Days. His aggressiveness was just what the situation required. But perhaps the South couldn't afford him in the long run.
Joe Johnston, the man Lee replaced, would probably have followed the course of action that you suggested. He was not as brilliant as Lee, but he was a solid general. Alas, he never held the confidence of Jeff Davis.
Washington didn't just wait for the enemy to come to him.
In Boston, he pressed an encirclement and caused the enemy to retreat.
New York did not go well, but it was Washington who pressed into the City for the fight.
The attack on Trenton was bold, and an important turning point.
To the extent that Saratoga can be credited to Washington's overall strategic plan: keep Howe facing him, to let Schuyler, then Gates, amass the militia and cut-off Burgoyne, although Washington didn't pass to the attack, he kept the enemy fascinated with him long enough to prevent the enemy from using the one wing of his army to rescue the other.