To give George Meade his due:
Meade had been in command of the Army of the Potomac for only two or three days before the battle opened. When he was awaken in the middle of the night to be told he had been appointed to command his first reaction was that he was being arrested. He was working with Joe Hooker’s chief of staff, Dan Butterfield, who was probably resentful that Meade had replaced Hooker as the army commander. Butterfield certainly did Meade no favors during the Meade-Sickles controversy.
Gettysburg was a classic meeting engagement where element of the opposing forces blundered into each other and everyone else then piled in as fast as they could. In the face of that and in the face of Dan Sickles going off on a frolic of his own to the endangerment of the Little Round Top - Cemetery Hill position on the second day, he kept his head and managed the battle and the army better than any commander had up until that time.
Between dead, wounded, captured and men who had simply been knocked lose from their units Meade had probably lost a third of his force by the time the three day fight was over. Of the seven army corps of the A of P two were no longer effective (First and Third) and three more had been badly beaten up (Second, Fifth and Eleventh). Only one, the Sixth was fully effective. Of his seven corps commanders, Reynolds was dead and Hancock and Sickles were dreadfully wounded. The A of P was badly beaten up – admittedly not as badly as Lee’s Army of Northern Virginia, but still in sorry shape.
By holding position on the fourth day Lee was able to give his logistical trains a 24 hour lead when Lee did begin his retreat into Maryland.
The weather and the unpaved roads conspired against Meade and significantly hampered his pursuit. When the A of P marched south from Gettysburg it was the fourth army to use those roads and to a great extent thy had been turned into bogs. When an army consisted of several scores of thousands of men walking with their weapons, ammunition, rations and water carried on the person bad roads counted for a lot and significantly restricted how far the army could travel in any 24 hour period.
Meade did catch up with Lee’s main force At Falling Waters, Maryland, as Lee was attempting to ford the Potomac some 10 days later but declined the opportunity to make a frontal assault on prepared positions. The memory of Fredericksburg was too fresh.
I suppose that had Meade been prepared to risk everything on one great attack at Falling Waters the war could have ended then and there. His corps commanders, however, advised against it, Meade was new in command and the risk was substantial that if the attack failed the A of P would dissolve right there.
As others have pointed out, Lincoln and Grant retained sufficient confidence in Meade that he retained command of the A of P , albeit under Grant’s immediate observation, for the rest of the war.
But Meade was the commander. He gets the credit for winning at Gettysburg so he also gets the blame for not destroying Lee’s army and ending the war in mid-July 1863.