Based on my nearly non existent knowledge of African hunting, I don't think the law allows hunting of the "big 5" with anything less than a .375 ...so in that regard, I guess a 30-06 would not "work", although I am sure that all these species have been killed by a 30-06 or some equivalent at some point.
WDM Bell shot elephants with a 7x57....everyone thinks they know that story. Eleanor O'Connor shot lions, tigers and maybe an elephant or two with her 30-06. Col Patterson killed the lions of Tsavo with a .303 British....which is like a 30-06 youth load. No "trophy fees" in those days and as long as they did not get stomped or clawed I doubt people in those times were too worried about wounding critters, especially those that were making a nuisance of themselves.
More recently, I remember reading about a gun writer who got a special permit to kill a Cape Buffalo with a 30-06....I think he used solid bullets. He posed with a dead buff so I guess he got it done.
"Men must be governed by God or they will be ruled by tyrants". --- William Penn
