This thread started out with the words "I know that no .30 Cal is considered a stopping round"
I am not so sure. I can't say what is the most popular round used by residents in Alaska today for big bears, but from the 1950s until 1990 it was the 30-06 and by far the favored bullets were 200 grain round nose. I'd be interested to see what was the #1 choice in Canada for the same years, but my guess is that it would be a 303 Brit or a 30-06 there too.
What is considered a stopping round is less about the round and more about who is doing the considering.
My sister lives in Alaska so I have been up there hunting a few times and if I were to go today I'd choose one of my larger and more powerful rifles, BUT if I were to find myself up there with any of my rifles from a 270 up to my 404 Jeffery and all those in-between I'd not feel under-armed with any of them ------ as long as I got to choose what bullet I was loaded and zeroed with.
Stopping any aggressive animal is first about placement and 2nd about straight line pentation, bone included.
Having killed many horses and cattle with a 270 Winchester I know what it's capable of doing with good bullets. In addition to horses and cattle I have killed animals from American bison, buffalo, moose, hippo, elephant and Kudu, a whole lot of elk, and a lot of others, I can say with no reservations I have learned about what works and what doesn't. In Africa I use 4 calibers. 308, 7X64, 8X68 and 404 Jeffery. I never had any problem with any of them either.
I own or have owned rifles up to 460 G&A and black powder rifles up to 8 bore. (I have made but not hunted with 4 bores, a 2 bore and also a 500 Jeffery and a 505 Gibbs) I kinda-like big rifles and as a rule I lean toward larger bore sizes. BUT experience has proven to be that it's far more important to have a bullet that holds together and a person shooting who has skill under pressure.
My nephew is a pilot in Alaska. As an illustration to my conviction of what I am saying, if he were to come down and land here and tell me to get in the plane to go hunting and I could take any rifle I have, from my 270 Winchester up, I would not even hesitate to get in the plane and go. Would I feel OK about facing down a mad bear with my 270. Yes I would!
That's not to say I would not choose one of my 9.3 or my 375H&H, or even my 404 if I had the chance, but the idea that I would just not be OK with a 270, 30-06, 308, 300 H&H, 8X57 or 358 Win is just untrue. ALL will do fine given good bullets and a cool head behind the rifle.
As a side note: My Sister has a Winchester M88 in 308 I got for her when she moved up there. In the years she's been there she has killed almost all her game with it including 3 brown bears. Caribou and moose too. All 3 bears have been one shot kills. I load her ammo and used 180 Gr Nosler Partitions.
No problem with any animal yet from 1988 to last year. Still going strong.
