Couple of years ago, fall of 2016, I used my 30-06 and one handload for four species:
mule deer @ 140 yards, one shot drop, had to administer a finishing shot when I walked up on it
antelope @ 245 yards, one shot kill
black bear @ 325 yards, one shot kill
cow elk @ 338 yards, one shot kill
Load was the 165 gr Nosler Ballistic Tip over a max charge of H4350, for good velocity and excellent accuracy. That 165 gr Nosler Ballistic Tip is a tougher bullet than many imagine.
If I was contemplating a bullet more for elk, moose & bear, I'd change up to the 165 Nosler Partition, or perhaps one of the many 180 gr bullets available. The ol' 30-06 is a great cartridge for the hunter, and will do most of what needs to be done afield.
Regards, Guy