Caution? Sure. Wisdom? Better.
Lee was a more tacticly perfect General than Grant and Gettisburg was not their first meeting.
Grants strategy of grinding down the opponent persistantly exploited his advantage in numbers.
But generally they were evenly matched , if Lee had withdrawn from Gettisburg he would have had to fight in another burg pretty soon , Grants greater ability to replace losses would mean that if Grant failed to break the southern force at Gettisburg he would eventually do so somewhere.
Lee knew that time was on Grants side, if Gettisburg had of been a defeat for Grant on the scale of Cold Harbor then the resolve of the North to fight might have been broken .
But at Cold Harbor Grant had long supply lines and Lee had short ones Lee's retreat at Cold Harbor left Grant in possession of a useless feild.
If Lee had retreated from Gettisburg where would he have gone to get a diffrent result?
I think that the Battle at Gettisburg and the Battle of the Bulge have some of these things in common.
The side fated to loose was staring at a disadvantage in trends and was hoping for a great reversal in trends with a big effort.
At present is time on our side?