Interesting. I was just reading Grant's memoirs this afternoon as he criticized the failure to pursue following the victory at Molino del Rey outside Mexico City.
He had more than the failure to pursue to criticize about that battle. He questioned the need to assault Molino del Rey and Chapultepec and would have bypassed them. Of course he was speaking years later with the benefit of hindsight and senior rank and reputation.
I tend to agree with his thoughts on not assaulting the strong points when they could have been appointed, principles set out by Sun Tzu.
Grant seems to have had an axiom that it is always good practice to follow a retreating enemy. That axiom ought to be followed with a great deal of caution. It could lead you into an ambush. Hot pursuit might temp you to outrun your logistics. Intemperate hot pursuit could string out your forces such that you lose cohesion of command and control. OTOH, failure to follow up could lead to a failure to consolidate a victory. The field of battle is not a chess board.
On the subject, consider that Spruance was also criticized for failure to pursue Yamamoto at Midway. I submit that Spruance was correct.
Consider Wellington at Waterloo following the French sauve qui peut. His instructions:
"No cheering, my lads. Forward and complete your victory."
In the time of the "thin red line" and the "British square" as battle formations it was axiomatic that you never let your men run, especially in pursuit of a fleeing enemy.