Actually, I think you'll find many who will disagree with you. Had the 20th Maine run, the outcome of the war could have been considerably different.
Would the South have won? Maybe not, but the peace would have been much more equitable.
I don't think so. They would have retreated back to the ridge, where the Union guns were firing effectively down the draw. They could have held up the advance there, with a combination of entrenched musket and cannon fire, if the Union guns were diverted to the flank. That would have bought enough time for the boys in blue to beat a hasty retreat and avoid being captured or decimated by the Confederates. They could have retreated across the river the same way Lee did, and lived to fight another day.
the peace would have been much more equitable.
At the risk of igniting the war all over again, what was so inequitable about the peace? The destruction of the South came as a byproduct of the war, not the armistice.
How much more equitable could it have been? Take any other rebellion in history that you care to mention and compare the fate of the losing side in that cause with what happened to the south.