So if I can pump 3 or more shots into an intruder with my 22 pistol at point blank range is this as potent as one shot from a 9mm or 45?
It all depends on where you place those shots. And the question is little pointless; at close range you're going to be able to get off a lot more than one shot of 9mm/.45 in the same amount of time as three shots of .22 LR. I can hit a silhouette target center mass with a 9mm almost as fast as I can with a .22.
But let's pretend that this ratio is accurate and that three shots from a .22 is the same as one shot from a 9mm. That would mean that to equal the capacity of a Glock 19 you would need a .22 pistol with a 45-round magazine. Also, I think the goal of any self-defense shooting should be to put two or three rounds into the center mass of your attacker as quickly as possible. If we keep using our ratio, that means you'll be using up to nine rounds per attacker with a .22, and most .22 pistols only hold ten rounds.
A .22 is not a self-defense round. Sure, it can cause wounds that can eventually be lethal, and it can even stop the threat immediately in some cases; but compared to a 9mm, .40, or .45 it is extremely deficient at immediately stopping a threat.