"Proofing" has tangible performance benefits where rifles are concerned and these are rooted in a nifty property of steels known as strain (or work) hardening. Did you ever wonder why, when looking at the properties of raw materials (of the same alloy), that cold-finished material has a higher yield and ultimate strength than the hot-rolled version of the same alloy. The answer is strain-hardening induced in the cold-worked version. This being a mere blog, I won't get into the eye-glazing specifics, rather I will attempt a layman's explanation. But, before we get into that, some definitions are in order because the following terms are often used interchangeably, which should never be done.
Stress = force applied
Strain = reaction to the applied force
Yield strength = the maximum stress that a material can withstand and still return to its original dimensions
Ultimate strength = the stress at which the material will fail
Elastic Deformation = the maximum strain a material can endure and return to its original form/shape/dimensions
Plastic Deformation = the strain at which the material will permanently deform
Now that that's out of the way, let's take a look at what happens to a rifle when it's fired with a higher-than-normal-service-pressure (proof) cartridge. I'll use small round numbers for simplicity, just for illustration. The actual numbers will vary with material, dimensions, etc.
Say we have a piece of steel that has an elastic limit (yield limit) of (to use round numbers) 1000 psi. Obviously, that means that it will return to its original form if any force of 1000 psi or less is applied.
If we apply and then remove a force of 1002 psi (0.20% beyond elastic limit), it will plastically deform, but only slightly (in fact, barely measurably) BUT, the elastic range has now been RAISED to 1002 psi. Meaning, that it will return to its present form if a force of 1002 psi or less is applied. The benefit is obvious as applied to locking surfaces but it's in the chamber where this phenomenon is truly valuable.
The rifle barrel, being by definition a thick-walled tube (any tube where the wall exceeds roughly 10% of I.D.), experiences this strain hardening in a very interesting and useful way.
When the chamber expands radially during the firing of an overpressure load (proof load), the inner portion (varies with barrel metallurgy, dimensions and chamber pressure applied) will be stressed into its range of plastic deformation, but the outer portion of the barrel (due to the great wall thickness) will be still well within its elastic range because the boundary of plastic deformation is still well within the barrel's outside diameter. What this means is that after the pressure event of proofing, the outer wall of the barrel tries to contract back to its original dimension but since the chamber has been plastically deformed, it (the chamber) will not contract, thus putting the chamber in compressive stress, which is highly desirable. This is exactly why a button-rifled barrel shouldn't be recontoured or fluted after rifling (because it alters the compressive stresses in the barrel).
Because of this compressive stress, it will now take an even higher pressure before the barrel yields again.
This applies as long as we stay within about the first 0.20% of the plastic deformation range.
Now a shotgun barrel is different situation entirely. Being of thin-walled construction, any "proof" cartridge capable of straining the chamber beyond its elastic limit would, almost certainly, result in a permanently bulged chamber, simply because the shotgun's barrel lacks the bulk material to contain the plastically deformed chamber within an elastically deformed "outer ring" of barrel. Even if this were not the case, it is unlikely that a shotgun would benefit from it, due to the shotgun's low operating pressures. In fact, I have encountered a certain classic-era American maker's guns in 16 gauge with bulged chambers on more than a few occasions (often enough to take notice of it), no doubt attributable to "proof-testing".
Where rifles are concerned, proof isn't just "testing for safety", it is part and parcel of the building of the rifle and integral to extracting the maximum performance from the system. The steel that the rifle is made from is materially altered in a beneficial way. Proof "testing" in shotguns seems to be just that, "testing", to see if it will blow up or not. Shotguns are, by design, low-pressure systems (far lower than even the lowest pressure rifle cartridge) and as long as all parts of that system are designed to contain strain levels well within their materials' elastic range, are made of quality material and exhibit good workmanship, the danger of failure is remote. Any shotgun is subject to failure due to a faulty reload or obstructed bore (as is any rifle) but such incidents fall squarely into the category of "operator error", against which there is no proof test. Proof testing may have had some value in separating the defective parts from the good ones back in the days when metallurgy was more guesswork than science but thankfully, modern metallurgy and (material science in general) is not what it once was.
More than one perfectly serviceable shotgun has been destroyed by "reproofing". Does this prove that the gun was unsafe to begin with? Maybe, but then again, maybe not. Shotguns are often designed to be lightweight and intentionally overstressing a shotgun with forces it was never designed to cope with doesn't really "prove" anything, whether or not the gun fails catastrophically. It is entirely conceivable that proof-testing an otherwise serviceable shotgun could induce damage that did not previously exist. Does this prove a fault in the gun's design or materials? Considering that a shotgun can not benefit from proofing in the way that a rifle does, it seems that proof-testing of shotguns is little more than willful abuse to gain a "peace of mind" that may well be illusory.