I can think of plenty of reasons why it would be easier to just lie and tell firing squads that one of them received a blank instead of actually receiving a blank round.
The cost of confusing blanks with live ammunition in a combat situation would be very high
Were there no outside indicators separating live from blank rounds?
Shooters couldn't tell the difference between firing a blank vs live round?
Responsibility is sufficiently diffused by just telling firing squads one of them received a blank round.
How do we know firing squads actually had 1 blank round instead of that just being a convenient lie told by commanding officers?
It's hard to confuse a blank with a live round. Blanks actually look different. Here are some British .303 blanks and here are some US 30-06 blanks. Notice that they're not only shorter, have a crimp instead of a bullet, but are marked with red paint. That's because blanks were used on the battlefield, employed when a rifle was fitted with a grenade launcher. Yes, to have a bullet encounter the grenade launcher and grenade there at the muzzle was a bad thing, so it was very important not to have blanks confused with live rounds. There is also the problem of recoil: a blank has almost none. With the M1 Garand, also, the rifle also wouldn't eject the spent cartridge. So, even if the firing squad was given their rifles with cartridges already chambered, it would be very hard for someone not to notice they'd fired a blank.
For the only execution by firing squad of a US soldier, Eddie Slovik, it seems to have happened. William Huie, The Execution of Private Slovik, stated that one of Slovik's 12 man firing squad had been given a blank. One of the judges in Slovik's trial, Benedict Kimmelman, also states this : he says
Twelve expert riflemen, strangers to Slovik, were detailed to the firing squad. They were rehearsed the day before. Slovik needed no assistance and replied quietly to those trussing him up and placing the hood over his head. He stood “straight as could be” without “any sign of emotion,” in the words of one of the squad. When the military surgeon examined the slumped body, following the volley of rifle shots, Slovik was still alive. None of the eleven bullets (one unknown rifleman having drawn a blank), fired from a distance of twenty paces by expert riflemen perfectly capable of hitting a silver dollar on a stationary target at twice that distance, had exactly hit the heart. He died as the guns were being reloaded.
So, one soldier knew he had fired a blank, and the other eleven knew they had fired live rounds ( and, obviously, because they knew it, those eleven were not aiming very well ) . But, importantly, no one other than those twelve knew. No one else could later claim, with certainty, that any particular soldier in the squad had shot Slovik. Call it plausible deniability.
As a follow up to that reply - Why did all of the riflemen miss?