The title states "all around deer hunting cartridge." Yes, moose are the largest of the deer family, but I can't find any source that lists coyotes as a part of the deer family. I would also bet that outside of Alaska residents, the great majority of US hunters will never hunt a moose.
For about the first 10 years of my "big game hunting career", I used my .30-06 for everything from prairie dogs, coyotes, mule and whitetail deer, pronghorn antelope, and elk. That was also my only centerfire rifle.
Then in the late '70s, after I had moved to Montana, and my new hunting partner here showed me that there were other hunting cartridges available other than a .30-06.
He showed me a .30 Gibbs case, and I thought that case looked so cool that I had my .30-06 re-chambered to .30 Gibbs. For the next 20 or so years, that was my primary elk cartridge. That's also the only cartridge that I actually shot both a coyote and a moose with.
For my deer and deer size animals (antelope and mountain sheep) hunting, I built a .257 Ackley Improved. I also shot my 2nd best 6x6 bull elk with that rifle, and a bunch of coyotes and a lot of prairie dogs.
For my varmint hunting, I built a .22-250 and besides coyotes and prairie dogs, I've shot a few deer and antelope with that rifle.
In 2009 I built my .300 Weatherby for my new primary elk rifle. Last September I shot a Canadian moose with the rifle and a 180 gr Barnes TTSX bullet. In Africa, I've shot a number of coyote size, or smaller, animals with that rifle. If I had that rifle on an elk hunt and saw a coyote, I wouldn't hesitate to shoot a coyote with it, but that rifle would not be my first choice if I was just going on a coyote hunt.