You'll notice where the muzzle energy has a break point between Grizzly Bear and Elk. As indicated, the recommendation column is for hunting, or put another way, one shot stopping power.
I am sorry, but you have obviously misread too much detail into the data and are now trying to extract a very specific answer, which is not available from the information given. Why? Primarily because ft lbs are not the be all to end all of hunting performance. It is but one factor of many factors.
And let's say we call it "one shot stopping power" which they did not do in the article. Lots of hunters are not prone to taking more shots than necessary. So they are more than happy to shoot an animal once and track it to where it finally died. In the case of bears, hunters have been attacked after finding their dead bears after a long stalk, only to discover the bear isn't dead. More than likely, the bear is going to die, the deer are going to die, with one shot, if you wait long enough. That isn't helpful from a self defense perspective. You are trying to extrapolate hunting data to self defense circumstances and that just isn't going to work.
Imagine a scenario where you have a semi-auto .308 battle rifle, (AR-10, SCAR, M1A, etc) and a grizzly is charging you. According to conventional wisdom, a single shot won't stop it. But would two? Three?
Conventional wisdom? What conventional wisdom? A chart you saw online with highly debatable information?
"On this chart, you’ll see the name of the cartridge, the caliber measurement for that cartridge, then an approximation of how big of an animal that cartridge could kill (much of which is highly debatable)"
You can kill a grizzly bear with a long sewing needle, if you know what you are doing. Bella Twin took a (at the time) record grizzly with a .22 long. Granted, she sniped it from very close range, but the point is that if you can penetrate into the interior of the animal by a few inches in the right spots, you can kill it. So for your .308 example, a .308 will readily kill a grizzly with an upper CNS shot and it will drop dead on the spot where it was hit (plus the momentum of the speed it was moving). You could easily double lung the bear and kill it just as dead, but that might take 30 seconds or more and in that time, the bear may chomp you several times, possibly killing you. The same goes for liver and heart shots, longer for the liver, quite possibly.
Of course, you could graze it off the shoulder or gut shoot it with a .50 BMG and not kill it or not kill it very quickly.
Bottom line, the ft lbs of a given caliber isn't what will save you. However, the more powerful the caliber, the greater the likelihood for more tissue damage. More tissue damage means having the potential benefit of causing the animal to collapse sooner or simply be dissuaded with a shot that isn't immediately lethal.
Then there is hydrostatic shock. The theory on how this works is somewhat vague in terms of specifics. There is some relationship between velocity, caliber (size or weight?), ft lbs, etc. and shot location as well as animal size and potentially other factors such as whether the animal is inhaling, holding, exhaling or holding when shot and even the direction of the shot in the body. Hydrostatic shock is the remote wounding of tissues by and insult such as a bullet. So if I shoot you in the left side of the chest, but I manage to burst the blood vessels in the right eye (nowhere close to the bullet's trajectory), that likely would be due to hydrostatic shock, but we want to burst the blood vessels in the upper CNS, not the eye. All you need to do is significantly damage the brain or upper spine to get an effective stop. It happens. The problem is that it happens with inconsistent reliability. Larger and faster (also heavier?) calibers tend to do this more often for a given size of animal, but not always reliably.
Depending on how you address the situation, you may want hardcast and deep penetrating bullets to break bone or you may want expanding bullets to do more tissue damage (different theories). Either way, if a bear is charging you, chances are you are not going to be making precisely placed shots. You will be rushed, scared, and if you aren't alone, your dogs will be barking or your partner(s) will be yelling and screaming at you, the bear, themselves as you are doing the same and trying to get your rifle on target. The target will be in motion, possibly straight at you, but bouncing up and down, possibly quartering toward you (oblique charge). It may be charging you on level ground which might be best for aiming, but it could be coming up hill at you, or down hill at you. You probably won't have time to rest your rifle on a nice steady tree or tripod.
How many shots you are able to get off will depend on your proficiency with the rifle, type of rifle, how many rounds it will hold, and how far away the bear was when you brought the rifle into the fight (timing). How many times you hit the bear will depend on how many times you were even able to fire and that will be your max possible hits. Most hunters are not trained or practiced in hitting moving targets. Most hunters are not shooting out of fear of being killed. Chances are that you will miss with one or more rounds.
So this is where it gets interesting. Larger, more powerful calibers are more apt to stop a charging bear, all other factors being equal, but they aren't equal. People tend to flinch and miss more with larger calibers. Larger calibers often come with increased handling weight, increased recoil, slower followup shots, and potentially reduced magazine capacity (if you aren't already government limited to X rounds). If you get a lightweight rifle in a large caliber, then the recoil will be even more pronounced, flinch will potentially be worse, and followup shots even slower.
So it is all a balancing act between what you can carry, what you can shoot well, what sort of performance you want from your bullets, your skills, knowledge of anatomy, etc.
