The .30'06 can serve for all North American game, but a more realistic minimal arsenal would have a .22LR rifle and a .375 H&H Mag.
It's true the argument I've heard in favor of the .375 H&H as the ultimate all-around gun has been on a more world-wide basis. But even for North America it has its advantages. In a CZ 550 safari or similar platform recoil is no worse than a .30'06. Rounds are expensive, it's true, but components are not. The .375 H&H loads up with standard powders very nicely and is able to work well with a wide array of them.
I think you're correct though for N. America.