If a person can calmly and accurately place a shot well enough to hit a target the size of a grapefruit,and if they are at a reasonable range,()like the typical 100 yds or less of real hunting,and if a person has the self dicipline to say"No,not yet,things aren't quite right"
With the proper bullet, a cartridge like the .257 Roberts will make it through the ribs and into the heart lungs of darn near all lower 48 critters.
For elk,I carry a bigger rifle,but I have a high degree of confidence I could take an elk with my .257 and a 120 gr Nosler partition.
I am not trying to sell anyone a .257,I'm saying the 30-06 ,used the same way,will certainly get the job done.