See I'm in the boat of owning both a 3 and 7mm08.
All throughout the shortages of late there has always been 308 ammo available. The rifles to fire it not so plentiful.
7mm08 however there have been rifles but limited at best ammo to shoot through said rifles. The 7mm08 is here to stay but if you want something that's roughly speaking similar performance just got with a 308 and get a decent recoil pad and good suppressor to help mitigate the slightly increased recoil. The deer won't tell the difference.
As a example Winchester Australia supply both the Aus and NZ markets, the Ozzies don't really use 7mm08 much but 308 is a different proposition so hence the supply of 308 Winchester factory ammo and not 7mm08.
I don't think it's a dying calibre per se but if you see all the fads and trends over the years there is one calibre that is the constant against which others are measured and is here to stay- 308 win.
I hope I've answered you're question as best as I can from what I know.
Bookmarks