Here is a story about excess headspace from Bob Greenleaf, who is a retired Savage engineer. He designed the post-Brewer version of the 110 action.
Bob took a 110 off the line in .30-06. With the lock nut breeching sytem the experiment was easy to do. All firing was done under controlled conditions.
He proceeded to fire the rifle, unscrewing and locking the barrel between shots. The headspace was increased in controlled stages, starting with standard. He stopped the test when it was impossible to get the rifle to fire any more, because the cartridge was so far away from the boltface and the firing pin. That is, headspace was grossly excessive.
The results of this experiment?
Nothing happened. Every case fireformed. No cases failed. No head separations.
Now, this test was conducted with fresh commercial ammunition.
No cases were reloaded, nor were they suitable for reloading. The ones from the later stages of the testing were stretched.
Does this mean that headspace doesn't matter? Of course not.
It is desirable that a firearm be within tolerances. If a cartridge case separates, some actions do not handle the situation very well.
Ever had a case separation in a .303? If you handload you probably have experienced this. Did anything happen, apart from the front of the case being left in the chamber? Was there a catastrophic release of gas? Or did you not notice until you tried to chamber the next round?
By all means, have each and every firearm you own checked for headspace, both commercial and military.