We somehow veered into this discussion in the comments of the previous post. I have an hour to kill in an airport lounge, so I figured I'll go find a good explanation of why the ubiquitous "government profile" barrel ended up the illogical mess that it is.
I vaguely remembered that Matt has talked about it and it turned out that, for once, my memory was spot on:
https://www.everydaymarksman.co/equipment/government-profile-barrel/
Over the years, I have talked to quite a few people about barrel profiles, encompassing both barrel manufacturers and AR-15 builders.
My basic question was simple: "where do you remove metal on a barrel if you are trying to save weight?"
In the meantime, since I have had a chance to build a significant number of ARs over the years, with most of them being fairly light, I have looked very carefully at how different profiles behave when warmed up. Now, they were not all made by same makers, but there are still some noticeable trends.
I have looked at barrels ranging from budget to expensive. Off the top of my head, I can think of AR Performance, Faxon, Voodoo/Adams Arms, Ballistic Advantage, Proof research, Criterion, Shilen, Green Mountain, AR-Stoner, Fulton Armory, Noveske, CMMG, Odin Works, Christensen Arms, Seekins. There may be others that I do not remember. With most of these, I have messed with more than one.
It is all anecdotal evidence, but still evidence.
With all barrels, when they get hot, the dispersion goes up. That's a given. What I was mostly looking for is whether the centroid of the group would shift significantly. In general, that is where more expensive barrels that are properly stress relieved have a decisive edge. There are notable exception to that, however. For example, I have never seen a Christensen barrel that would not have a comparatively massive shift when warming up. At this stage in the game, unless they changed something drastic, I won't touch one.
Another clear trend is that barrels that have some extra material left near the chamber do better. The most drastic example of that was the ultralight barrel from Voodoo/Adams Arms (before they reinvented themselves). It is essentially a thin noodle of a pencil barrel except on the back end of the barrel near the chamber, the full length portion extends forward by an extra couple of inches. Toward the front, everything is seriously thinned out. When hot, groups open up, but they do not wander.
The same trend continued with other makes with no exceptions that I have seen. If you want stability of POI centroid, you need to have extra metal near the chamber. The feedback from the industry was pretty much the same.
Why then does the government profile (thinned out under the handguard and right in front of the chamber, while a bit thicker in front of the gas block) persist? People are asking for it because it is used by the military. That's it. There is no other reason. In other words, if it wasn't for the government's massive bureaucratic inertia, it would have been long gone.