But what Rhea points out (and other historians have pointed out) is that no general in the Civil War had the insight to realize the tactics of "frontal assault" against a fortified enemy position were simply wrong with the advent of the rifle. The rifle had changed the tactics of combat but no one in the Civil War realized this (they didn't even realize it in World War I, really - as military historian General J.F.C. Fuller pointed out in his "The Generalship of Ulysses S. Grant").
The idea was, you got yourself into the best possible position, and when you felt you had enough strategic advantage, you threw your men at the enemy in a direct assault. The only differentiating factor was did the General ordering the assault have a good gauge of whether the assault had a reasonable chance of success. At Fredericksburg, no amount of men could have taken Marye's Heights - and Burnside wasn't smart enough to gauge this. Grant was much better at this, and he only ever ordered an assault when he felt he had a very good chance of success. Looking at his track record, he was right more often than not. On May 22nd, 1863 at Vicksburg, and on June 3, 1864 at Cold Harbor, it didn't work.
However, at the Mule Shoe at Spotsylvania, he almost succeeded in wiping Lee out. If Gordon hadn't led such an amazing resistance and counterattack when he did, the Confederate army would have been in the sh!t. Hancock would have ran right over them. Again, Burnside let everyone down.
So Grant is no more to fault for this than Lee or anyone else when it comes to using frontal assault tactics. Lee deserves more blame for Pickett's Charge than Grant does for Cold Harbor. Pickett's Charge is a far more obvious tactical impossibility - one that rates with the obviousness of Fredericksburg. Lee, however, was caught up in the idea of the invincibility of his army - that was his blunder - he felt they could do anything he asked of them.
What's key is that Grant never tried such an assault again after Cold Harbor.
In the end, it was Grant's grand strategy that beat Lee and the Confederacy.
Grant paid a price of his "hands off" policy with Burnside, then gained it back two-fold with Sherman.