I'm going to be out of the house today with my carry gun, so I'm going to intentionally shoot someone today with my carry gun, by your "logic". Actually, my goal is to never shoot anyone with it, so if by "intentionally shooting something", you mean "intending never to shoot something" then I guess you're right.
The rapidity of fire is a false narrative and you're only going to have time for so many shots.
You are 100% right that you'll only have time for so many shots, and the more the recoil/muzzle rise, the fewer the shots you'll have time for and the poorer the quality of the followups. This is why all the practical pistol competitions regulate scoring by power factor--a scaled version of momentum which relates directly to recoil. People shoot faster and better with calibers that don't recoil as much--there's really no room for debate on that. Given that fact, and the reality that defenders are going to miss and make less than perfect shots with a handgun when under high stress and shooting at a moving target, it doesn't make sense to unduly limit the number of shots that can be taken and the quality of those shots by going too high with recoil. The sweet spot is cartridges that are demonstrably capable of ending the threat but that don't incur too much of a recoil penalty.
If "bear shot with 10mm, shooter lived" is enough for you...
Well, yeah, by definition, "...shooter lived..." is successful self-defense. More details is always good, but the bottom line is that we can see it has worked, and we can see by the penetration figures that it is capable of working.
Go forth and shoot something 1000-1500lbs with a 10mm and report back on how good an idea it was.
I think that most people who are forced to use a handgun to defend themselves against a bear wouldn't do it again if they had the choice. In fact, I think that most people who haven't would rather that it stayed that way. That aside, we can see from the real world that 10mm and .45ACP work for bear self-defense.
#1 Bear attacked, was shot, ran away, defender survived. Successful self-defense.
#2 This was a successful self-defense, but it probably doesn't make sense to credit the pistol shots due to the rifle shot involved.
#3 Bear attacked, was shot, ran away, defender survived. Successful self-defense.
#4 Bear attacked, was shot, defender survived. Successful self-defense.
#5 Bear attacked, was shot defender survived. Successful self-defense.
#6 Bear attacked, was shot, defender survived. Successful self-defense.
#7 Not a great story, but the defender(s) did survive so that's still a success.
.45 Examples:
#1 Bear attacked, was shot, defender(s) survived. Successful self-defense.
#2 Bear attacked, was shot, defender survived. Successful self-defense.
#3 Bear attacked, defender survived. Successful self-defense.
And as you know, there have been incidents where even lighter calibers have been used successfully to stop grizzly attacks.
By any reasonable evaluation criteria, when the defender survives, that's successful self-defense. That's the standard we use for self-defense against human attacks. If the defender survives, we claim it's a success, even if we don't get all the details and even when the scenario doesn't play out like a movie script. Why should there be a different set of criteria for success when the attacker is a bear? Does it make sense to make up a different criteria for judging successful self-defense for bear attacks? I mean, I can understand how damaging it is to your position and why it would make sense for you to try to redefine terms to support your argument, but your dedication to your stance on the topic doesn't change reality.
Imagine if we looked at a human self-defense story where the defender survived and the attack was stopped and claimed that it was a failure because the attacker was shot too much, or because the attacker ran away instead of dropping on the spot, or because the attacker didn't immediately cease the attack, or because the attacker was gut shot and only died later, or because the defender emptied his pistol and the attacker was never found. Clearly that would make no sense at all, just as it makes no sense at all here.