[BroJoeK]

jeffersondem: "Grant (if he had been there; he wasn’t) would not have hesitated to take another 20,000 Union casualties in order to inflict another 2,000 Confederate casualties."

Which brings up an interesting point, often overlooked.
At Chancellorsville itself, Lee's force was less than half the size of Hooker's, and yet Lee suffered more casualties and deaths than Hooker's forces.
22% of Lee's 60,000 troops were casualties = 12,764 including 1,665 killed in action.
9% of Hooker's troops were casualties = 12,145 including 1,082 killed in action.

Numbers & percents change somewhat if you consider the whole Chancellorsville campaign.

By my count, Lee lost two generals killed and nine wounded.
Hooker also lost two generals killed, plus three wounded.

Here is one description:

"Lee, despite being outnumbered by a ratio of over two to one, won arguably his greatest victory of the war, sometimes described as his "perfect battle."[74]

But he paid a terrible price for it, taking more casualties than he had lost in any previous battle, including the Confederate defeat at the Battle of Antietam.
With only 60,000 men engaged, he suffered 13,303 casualties (1,665 killed, 9,081 wounded, 2,018 missing),[11] losing some 22% of his force in the campaign—men that the Confederacy, with its limited manpower, could not replace.

Just as seriously, he lost his most aggressive field commander, Stonewall Jackson.
Brig. Gen. Elisha F. Paxton was the other Confederate general killed during the battle.

After Longstreet rejoined the main army, he was highly critical of Lee's strategy, saying that battles like Chancellorsville cost the Confederacy more men than it could afford to lose.[75]"

If we consider that the Union white population was four times greater than the Confederates, in terms of available manpower, losing one Confederate soldier was equivalent to losing four Union soldiers.
And yet, by some counts, Lee lost more at Chancellorsville than Hooker did.

Bottom line: in Civil War battles, attacking forces often suffered disproportionately more casualties and that certainly included Lee:

1. 22% at Chancellorsville in 1863.
   
2. 27% in the Maryland campaign 1862.
   
3. 39% at Gettysburg in 1863

Though, so far as I can tell, besides some grumbling from Longstreet, nobody thought to call Gen. Lee a "butcher".

[jeffersondem]

According to Wikipedia, Genral Lee himself shared your pessimistic view of the southern effort. Supposedly he wrote:

“At Chancellorsville we gained another victory; our people were wild with delight — I, on the contrary, was more depressed than after Fredericksburg; our loss was severe, and again we gained not an inch of ground and the enemy could not be pursued.”

But he bought time for the South, and under any number of circumstances, the extra years could have resulted in both victory for the South and saving the Union.

As we read the headlines today, we know both were lost.