This has been a long standing debate in bench rest circles (a discipline very removed from carrying a rifle around in the bush). The consensus is that it simply doesn’t make a difference, belt or not, with regard to accuracy. Some insist that cartridges without a belt are generally more accurate (David Tubb being one, and he is as much an authority as any), but there’s plenty of evidence to dispute the claim. Custom gun makers will generally ignore the belt when cutting a chamber, choosing instead to headspace off the shoulder, which is saying something, but again there’s many a backstory. As for resizing cases to headspace off the shoulder, there’s a number of reasons for doing so, reduced working of the brass a bit down the list. As for centering the case in the chamber, a belt does nothing of the sort for virgin brass (once fired, sized to headspace off the shoulder and not worked with a collet die, perhaps, but not on the first go around).
With regard to what we’re discussing, which is rifles for dangerous game, it’s totally a non-issue. The .375 H&H needs a belt for headspace. Most modern cartridges do not. Many still have a belt, though, a vestige the past. Some new, from the ground up designs also have a belt, often dimensionally unique (the .450 Marlin and .500 Wyoming Express being two such examples), but these exist for very specific reasons. As for the .416 Remington Magnum, it could easily and quite happily get along without its belt, but it’s there and does no harm. I do still consider the .404 Jeffrey superior in every sense (other than availability and cost, of loaded ammunition and components) and have my reasons for thinking so. It doesn’t mean I am right, only that, for now, I remain convinced.