I think that expecting the AOP to destroy the ANV in pursuit was not realistic.
1). Meade had been in command only a few days. Meade performed well at Gettysburg essentially coming off the bench. Expecting him to win the war to follow it up was a bit much.
2). The Union first corps, third corps and eleventh corps were so badly savaged as to not be combat effective. Only the sixth corps was intact.
3). Meade had lost his three most aggressive corps commanders: Reynolds, Hancock and Sickles. Sykes was new. Sedgwick was solid. Howard was irrelevant having a shattered command. Slocum was not horribly aggressive and his corps had suffered significant casualties.
4). The ANV was retreating over the mountainous terrain of south mountain. That limited the avenues for pursuit and gave good defensive positions for the rear guard.
5). There was the notion that a defeated army could be destroyed if pursued, but it just did not seem to work out. Grant made a pretty quick attack of Pemberton's defeated army at Vicksburg and that was a big failure.
Thomas was not able to successfully pursue the Army of Tennessee after Nashville.
6). Another fact was that in taking casualties, a unit's offensive power degraded far faster than its defensive cohesion. The defense is easier. You set up your line. The troops take advantage of what cover they have. When the other side comes, you shoot at them.
On the offense, It is not easy to launch a coordinated assault. If you have a shot up command structure with newly promoted officers in key positions, making a coordinated assault is a **** shoot.