Headspace is critical for safe functioning of a high power rifle.
The first consideration is the rifle case. The cartridge can only stretch so much than it will rupture. I believe I read it in Col Chin’s book that .006” is the standard maximum safe stretch. At least for a 20mm cannon round. After that the cartridge is highly likely to separate. The Brit’s called it case breakage if I remember right.
There is some confounding data out there, from P.O Ackley. He was able to fire 30-30’s without locking lugs and the case stayed put. I believe the chamber was very clean. Modern analysis of case stretching with a 308 shows how he got away with this.
http://www.thewellguidedbullet.com/mechanical_studies.htm "Yielding of brass case walls in Chamber" by James A. Boatright
Mr Boatright shows that around 25 K psia a 308 case head will stick to the chamber wall and hold the pressure. However above that pressure the side walls will stretch and if the case head is not supported, the case will rupture.
Another issue with excessive headspace is peening. Too much headspace and the case head will slam into the bolt face. This is a shock loading and can peen revolver shields, bolt lugs, receiver seats. It will be aggravated by low friction cartridges. I lubricate the cases used in my M1a. Eliminates case head separations which occur from case stretching on extraction. However I only set my shoulders back .003”. I suspect if I were to have more than .006” headspace difference between case and chamber I might have experienced peening. As it is, I am on my third barrel and everything is good.
Then there are issues with cases which are so long that they are a crush fit to the chamber. This is undesirable as it will cause an interference fit. The first problem is getting the bolt closed. You will read threads on this all the time, the guy does not use cartridge headspace gages to set up his dies and now he can't get the bolt to close. This will absolutely gum up a semi automatic mechanism. The second problem is getting the fat round out of the chamber. The interference fit will be worse after firing.
All modern rifles are checked for proper headspace at the factory. Surplus rifles must be assumed guilty till measured innocent, though if the surplus rifle has matching bolt and receiver numbers it is mostly likely OK.
Headspace is something that must be controlled between the ammunition and chamber for safe reliable functioning of a firearm.