The question becomes how many useful and safe reloads can one get from a case? Some belted mags, at peak pressure the chambering and extraction may become sticky after just one firing and resizing. Conventional sizing dies will not even touch the area in front of the belt-- the source of the problem. This can also be noticed in some standard rimless non-belted cases. There is a difference between headspacing shoulder setback and sizing the area just in form to the web. Two different things. Setting back the head spacing stop, the shoulder, on non-belted brass is the surest way to shorten case life just as is having excess head space in a chamber to begin with. IMO, use the belt for headspring on belted brass and don't try to rely on the shoulder. That doesn't mean set the shoulder back on a belted case either. There is a reason that cartridges with shallow or only false shoulders must have a belt. The 375 HH was designed with a belt for the reason of providing a sure and consistent headspacing stop.
Prudent, necessary sizing DOWN the area of the case body causing sticky chambering or extraction hardly contributes to reducing useful case life or case stretching. That happens from shoulder set back during sizing or the from basic headspace clearance needed for all cartridges to freely chamber without without resistance. Obviously, excess headspace will greatly reduce case life. But all cases have a finite, useful lifespan.
Actually a "small base" type die can easily be made by sacrificing a regular sizing die. For a belted mag, turn off base of the die to just forward of the belt recess. Lightly chamfer and smooth the entry. Then cut the front part of the die off just below the shoulder or false shoulder area of the case. This die will size right up to the belt and not touch any part of the shoulder.
I made such a die specifically for all the '06 family and similar cartridges like the 7x57 because occasionally even the non-belted cases will expand enough in the area just forward of the web to cause sticky chambering and/or extraction. Conventional dies will usually not resize that portion of the case. To do so, by forcing a case that far into a sizing die, would also severely set back the shoulder- not a good thing! There is a reason for the small base dies available for common lever action type cartridges. :)
For the belted mags, I use a dedicated collet type die made by Innovative Technologies that sizes only about a 1/2" portion just in front of the belt. The die is good for use for all standard belted mags in the family with a .532" head diameter. It's not a cheap die but neither is discarding belted mags after a sizing or two when they have several sizings of life left in them.
And of course all these sizing operations are adjustable and done only to the extent necessary for resistance free chambering. For DG ammo especially, not a good idea to have sticky chambering or extraction. For target shooting, many shooters prefer a "snug" fit for accuracy/concentricity purposes. Two different types shooting, two different types of ammo!