Bonanza,
Actually the numbers of double rifles produced between, say 1920-2000, were surprisingly small. I think a check of the books on British Gunmakers will bear that out.

I think there is a bright future for double rifles! They may not be British, but there will be double rifles.

As far as the 500/416 is concerned, I think it will become a classic double rifle round as soon as enough folks use it.
It provides the classic double rifle round features. A flanged case, delivers a large caliber bullet at moderate pressure. I can see where some would argue that it isn't a "Stopper". However when it comes to penetration that long .416 bullet is just the ticket. I can see the 500/416 used more than, say a 470 or a 500 as an all around double.

A friend has a Kreighoff in 500/416. He took it to Africa and it swatted all the game he could shoot with it.

If I were to by another double rifle, today, it would be chambered in either 500/416 or 475 #2 Jeffery.

Just my opine.