Simply because every moron on both sides was taking the wrong lessons from Napoleon and devising large scale plans with heroic charges. Grant and Meade might be the only competent generals serving in a major command in the entire war on both sides. Before you give me “Cold Harbor”… let’s honestly ask what was more costly… Union losses at Cold Harbor or Southern losses at Chancellorsville? Grant won the war because he realized what most didn’t… The Army of Northern Virginia might as well have been Hannibal’s army after Cannae. But Lee was a far lesser Hannibal.
Tactical contexts matter.
Lee was trying to destroy the AoP at Chancellorsville because an attritional model was a losing game for the Confederates.
Overall, Grant lost more men between 5 May and 15 June than Lee had in his entire army.
Grant gets credit for continuing the campaign, despite the carnage (He could afford the casualties. Lee could not).
Grant's system was (1) grossly outnumber your opponent (In the Vicksburg campaign, Grant had 150,000 men, Pemberton has 30,000; at the Wilderness, Grant had 118,700, Lee had 66,140) and (2) remain on the strategic offensive and never mind your casualties no matter how bad they are (see point 1). By the time they got to Petersburg, the Union VI Corps was the only one fit for attacking. The rest had been bled dry and could generally hold trenches, but could not attack them so Grant just stretched the lines further than Lee could (especially after the wave of Confederate desertion after Lincoln's re-election.
As for Grant's applicability for today, there are not many opponents the US can outmuscle and trade casualties at the rate of 17 US to 11 enemy and win. The US could in 1864, but those conditions are no longer applicable today.
Wade Hampton made what I find an convincing point. Keep the two sides exactly the same on May 5, 1864 (manpower, strategic objectives) and swap the commanders (and
only the commanders). A Grant-led ANV does not survive past Christmas.