I agree that it was customary of whomever commander abandoned the battlefield is the one who admitted defeat. However, the battle was over by “this morning”. He would later state that he, “just lost confidence in Joe Hooker”,but he most likely suffered a concussion and was mentally unfit to make command decisions. General Meade begged him on May 3rd & 4th to send in the Union 1st and 5th Corps, 37,000 fresh troops, but Hooker wouldn’t allow it and instead ordered a retreat.
One of the great “what if’s” is if Stonewall Jackson had not been wounded at Chancellorsville. But what if Joe Hooker had not been rendered ineffective by that artillery shell?
“But what if Joe Hooker had not been rendered ineffective by that artillery shell?”
No one can say, just speculate.
I will say this: getting a concussion was probably the worst thing that could have happened from the Union view.
If Hooker had been killed, a replacement commander would have been appointed. He probably could have done no worse; maybe better given the overwhelming Union advantage.
Grant (if he had been there; he wasn’t) would not have hesitated to take another 20,000 Union casualties in order to inflict another 2,000 Confederate casualties.