The story of the confederate retreat, the length of the “train”, carrying the wounded, in torrential rains, and the Union let them out.
They could have ended the war right there.
That was the biggest and costliest blunder of the war! Why did the union let Lee escape?
It was actually a theme throughout the Civil War, and not unique to the battle of Gettysburg. A few reasons for it....
Even the victors in most battles were beaten down and exhausted, and many times the victors suffered almost as many casualties as the losers.
Gettysburg may have been a decisive victory, but the casualty totals were 28,000 Confederate and 23,000 Union. Chancellorsville, a decided Confederate victory... 17,000 Union, 13,000 Confederate. Antietam was probably the North's best chance to end the war in a single day and they blew it. It was considered a Union victory, but casualty totals: 12,000 Union, 10,000 Confederate. The victories simply were
not one sided enough where one army then simply routed or cleaned up the other.
Contrast that to Austerlitz, considered one of Napoleon's best battles: French casualties about 8000 while the coalition forces lost about
27,000 killed, wounded or captured. A lot more decisive than most Civil War battles
So when you think about a battle like Gettysburg, where it is considered a fairly decisive Union victory, the Union army was not in much better shape than the Confederate. When you think about repulsing Pickett's charge, remember that the battles on the 1st and 2nd at places like Culp's Hill and Little Round Top were very near things.
When someone says, "Grant would have pursued"... well.....after his victory at Chattanooga, the Federal's attacked at Ringgold Gap, got beat and Grant gave up the pursuit.
The only example I can think of in the Civil War where one army simply wiped the other out was the Battle of Nashville, where the Union effectively ended the war in Tennessee. But that example was primarily the result of the stubbornness of John Bell Hood, who pursued the Federals to Nashville after
losing the Battle Of Franklin fairly badly.
Unlike in the Napoleonic Wars, the cavalry arm of both armies was weak. Despite the heroic exploits of the Stuarts, Bufords, etc, there was no true heavy cavalry in the US that could ride down a retreating enemy and decimate them. Cavalry in the Civil War armies was used more for scouting and raiding. Therefore, you were for the most part pursuing a retreating enemy with your
own tired, worn out infantry. It simply was not a recipe for removal of an enemy army from the field.