There is much truth in what you say. It also helped Grant to have greater resources of men and material than Lee. I am reminded of a passage in Attack and Die by Grady McWhiney and Perry Jamieson:
During the Atlanta campaign, Sherman said that he could not afford the losses that Grant had suffered on the offensive in Virginia. On May 22, 1864, he wrote of Grant's tactics, "Grant's battles in Virginia are fearful but necessary. Immense slaughter is necessary to prove that our Northern armies can and will fight."
I wonder what the outcome would have been if Lee had had the resources that Grant did. Maybe Lee would have simply ground down the other side expending manpower like Grant did.
Here is another perspective from Attack and Die:
Throughout the war Confederate leaders seemed to ignore the casualty lists and to mutilate themselves and their armies. A northern observer pointed out that "Southern leaders were, at least up to 1864, bolder in taking risks than their opponents, but also that they pushed their forces under fire very nearly to the limits of endurance." Such actions were justified, according to Confederate Colonel W. C. P. Breckinridge, because "it was the fate of the Southern armies to confront armies larger, better equipped, and admirably supplied. Unless we could by activity, audacity, aggressiveness, and skill overcome these advantages it was a mere matter of time as to the certain result. It was therefore the first requisite of a Confederate general that he should be willing to meet his antagonist on these unequal terms and on such terms make fight. He must of necessity take greater risks and assume grave responsibilities."
But in every war, one side always has greater resources than the other, but that advantage does not always equal success. Lee, and his early opponents, focused entirely on winning battles. But in every battle won, Lee lost a greater percentage of his resources than his opponents. It was a mathematical certainty that he would run out first. When Grant took command, he forced Lee's rate of expenditures even higher, eventually forcing Lee entirely off the field and into defensive trenches around Petersburg and a slow, certain last stand. Grant understood the math. Lee didn't, until it was too late.
Washington, at even much greater disadvantage than Lee, forced the enemy to spend resources in a higher proportion than he did. They were running out faster than him. I simply don't understand how Lee, a man who lived his life in the shadow of Washington, did not emulate his strategy better when faced with a similar situation.