For what this is worth:
I've been bedding rifles for over 20 years now and I like to think I've gotten pretty good at it. The debate over padding the barrel cylinder gets thrown back and forth quite often. I've done it as well and the only instance where I personally saw it make a viable difference was with Anschutz 54 actions used for International 3p shooting.
Why? I have my guesses, but they are not proven.
The Annie 54 is a small OD receiver, 1.150". Barrels typically used are 26" in length. Silly on a little piss ant 22 because all the powder is gone by 18". The reason they do is to get the sight radius "out there". The consequence is increased barrel time which makes the gun harder to shoot well. So, that trend evolved to backing off to 18" and adding all sorts of contraptions off the muzzle ring to get the sight radius increased again. Either way, you have mass hanging way, way off the moment and on a little receiver, that's not the best pathway.
So, adding a pad of material to help support it helps in that instance.
With center fire the game seems to change a bit. 1. Bullets are moving roughly 3x faster so they don't loiter around the way a 22 does. 2. receivers are typically larger in diameter so it helps to support the barrel mass a little more and it provides more surface area contact with the rifle stock.
If anyone has ever wondered why I go through the pains of being particular on the inletting work I do, that's a big reason. I like to have as much of the rifle stock in contact with the receiver as possible. -Just look at a bench rest rifle. Single shots, big stuff, and all squashed down into as much of the register as possible.
In 2003 the Brittish Fullbore team used 34" barrels on their Palma Rigs. None of them had barrel pads. Now, the actions were pretty robust (RPA Quadlocks), but it did not require additional support. They won the team event btw. I personally have a 300-338 lapua build on a 34" M24 contour stick that slings 125 grain bullets at 4375fps. Again, no barrel pad. That gun shoots 1/2 groups at 600 yards when the wind and sun play nice. My receiver is one I made from scratch and its 1.350" diameter. Nothing special about it other than being a CRF type setup.
Based on my experience, I don't see the benefit from it. What I do see however is another complicated problem to solve once the barrel gets pulled and replaced by another one. We all know that barrel makers don't spend a great deal of effort ensuring that the outside diameter runs on the same center as the hole. (concentricity) We also know they don't obsess over diameter fluctuation. Because of it the pad has to be enlarged and bedded again. Most just have me remove it completely when it comes time to do this.
Just something to think about.
