If I were to lay down the cash for an opportunity at a trophy elk, I'd want more than a 30-06.
For deer, hogs, and antelope, IMHO, the better BC of any of the 30-06's smaller-bored offspring, 25-06, 6.5-06, 270 Win, or 280 Rem, would be my preference.
And, for just sheer accuracy potential, I'd chose a 308 Win over the 30-06 any day.
Not saying the 30-06 wouldn't work, or that there aren't very accurate 30-06s out there. But 30-06 just wouldn't be my first choice for anything.