The .280Rem can shoot heavier bullets faster, so would there be as much bullet overlap as you think? And if there were overlap, why not just use the .280Rem for everything? And if you weren't interested in heavier bullets, why go with a .280 in the first place? This is one of the existential questions I wrestle with when dreaming about a custom 7x57 while I've got a perfectly good 7mm-08.
As far as my 7mm-08, I'm a big fan of the cartridge, but right now, I love shooting my Tikka, and it happens to be chambered in .260Remington - another fine whitetail cartridge. If something bigger than whitetail where on the menu, I'd switch over to my 7mm-08.