The grout adds an element of strength to the floor. As pointed out, the spaces between the tiles are much less likely to chip because the grout adds "support" to the tile edges. If you walk barefoot, you'll feel everyone of those ungrouted edges as well. And the prospect of fixing a few cracked tiles, even before the floor is grouted, creates further delay when you are ready to install the grout.
Use plywood if you have to move the heavy stuff back in. Cardboard is good for foot traffic.