It's also logical that dead soldiers can't carry anything. If the first row of troops is going to die anyway why not have them be the armored front to reduce as far as possible the number of casualties on the initial attack. But I do recognize all the good points against the idea: shrapnel, hits in the side , weight, would it stop a bullet anyway?
But look at the results without shields! Cold Harbor, Fredericksburg, Picketts Charge, Battery Wagner, Franklin and on and on. If I was the Secretary of War I know I would have been open to the idea of testing to find the lightest weight, highest protection shield in whatever form just to try it. And as the other poster showed with hemp bales and saps the troops thought of this to.
You may actually end up with more dead and wounded. Your pace would have to be slower and steady for the shields to be effective. You'd give artillery more time to devastate an attack force.
Better off using your time changing battlefield tactics.

