Reputable manufacturers ensure that they have barrel extensions and reaming depths correctly set-up before the guns are even test-fired, with the right amount of slop for a gas gun to run reliably.
Somehow, I have made it since 1988 never using a headspace gauge in the AR15, to include countless builds.
I do run a dummy cartridge in my chambers to see what’s going on with the throat location, so I know where I can load my COL with, and I also look at shoulder growth compared to a virgin case after the first round has been fired.
If you’re buying from Peasant-grade suppliers, then it might make sense, but why bother buying barrels from those sources anyway when you can get a well-engineered pipe from people that are way ahead of the power curve when it comes to headspacing.
The headspace would have to be insanely off to generate the kind of case stretch at the web you’re talking about. There’s a good article where some guys took an old bolt gun, and kept increasing the headspace intentionally to see where this really starts to matter. They had to re-size cases several times before they could get the case to fail, and the failures were very minimal, with slight signs of partial separation happening before anything else.
What is more problematic is when these cheap, after-market, non-engineered, fly-by-night companies start jumping on the “AR15” parts bandwagon, with almost no understanding of quality management. The more likely problem is that you will get a barrel marked “5.56 NATO”, when the reamer was so worn, that it cut an under-sized chamber.
Then you slap in that magazine of XM193 or XM855, or a foreign made 5.56 load with soft brass and lower standards of metalurgy in the brass alloy, which are also towards the upper end of pressures already in most cases. Now you chamber these cartridges into your worn reamer special barrel, which has a really tight and short throat, no matter how the reamer started out, and that 58-60ksi 5.56 load jams the projectile into the short-throated lands.
Pressures will spike on you bigtime, and the case will fail, even with correct headspace. The headspace gauge can detect this from the start, but so can a dummy cartridge with Dykem or marker. I always check if a cartridge will fall free from a chamber after pressing the cartridge fully into the chamber. If it doesn’t, I want to know why, and will start looking at that particular barrel more closely until I’m satisfied I know why.
Here’s a great example of a case failure that I think was caused by an under-sized chamber, as well as foreign-made brass: https://www.m4carbine.net/showthread.php?134302-Critical-Failure-Seeking-Advice/page13