Hi,
I doubt that, at least during WW1, German soldiers dared to modify their equipment without strict orders or written permission. Personal initiative was not considered to be a good thing in the German military (it still isn't in most European armies

).
The cup is suspended on a feeble piece of leather that will break or rot off after years of bad storage, I guess that is the main reason for so many of them getting lost. Getting the cup off, the pistol out and the stock in place takes less than half a minute, but you are right that they would have stocked the pistols some time before the real action began, not in the heat of the battle (no time to reach for the pistol anyway, hence the old shovel, stick, dagger, shoe, etc..).