That could work, but it would also render the sapper virtually useless considering his only viable job after that would be to construct fortifications with the hammer. And besides, imagine if 80% of the team had the capability to dig trenches. They would be spammed up the ass, and then the build-points would be wasted and the vast majority of the team wouldn't ever get to dig trenches.
I think it's fine to keep the shovel exclusive to sappers, and besides, individual soldiers did not carry shovels in the Napoleonic wars. Here's an excerpt from wikipedia:
Being too long and heavy to be transported by individual soldiers, entrenching shovels and spades were normally carried in the supply carts (logistics train) of a military column; only pioneer or engineer troops typically carried spades or shovels as part of their individual equipment.