I think the reasoning is fine. Its the conclusion I think is in error.
First off, there is no magic bullet. Nothing is a 100% one shot stopper 100% of the time.
Consider the premise. "Coming troubles..." (a nice way of skirting the forum rule about TEOTWAWKI discussions) but one that could be allowed, if you consider what has happened in riots and natural disasters...
Ok, now, the OP is looking at "hits needed to turn attacker(s) away from his home". Thats fine. But it ignores the effect of the hits, other than turning away an attacker. Or, rather, assumes all hits to be equal, based on the TV telling us about how multiple hits with the 5.56mm are needed. And, "turning away" is subtly different from "stopping" an attacker.
One should also consider the motivation of the attackers. Current combat is against religious fanatics, the majority of whom suscribe to the idea that death in battle against their enemies is a good thing. They don't want to stop, they want to kill the enemy, and/or die gloriously doing so.
Someone(s) attacking your home in the "coming troubles" won't be doing it for that reason. They'll be doing it to get something you have. Food, valuables, arms, or possibly even shelter. They will not be attaking your home seeking death in battle. The things they want will also be had in other places, so there is a high probability that after being shot (with anything) or even shot at, they will turn away and look for easier pickings.
To me, that's a significant difference. Someone getting hit 3-5 times (multiple whatever) with a .22LR might not be physically stopped but the odds are high that it will make an impression. And it will make an impression on those with them.
But, this is a double edged sword. Odds are high that they will turn away, but there is also a risk that not doing significant damage with a round or two will enrage the group and intensify their will to attack. (OMG they shot Kenny! You B*********! Get "EM!, etc...)
You can have a lot more ammo for the same cost with a .22LR, and you can trust that lots of hits with it will do the job. But be prepared for the real world to have a different opinion.
Go ahead and stock up on .22LR (and guns, because A) having only one gun is a point failure source) and B) grabbing a second loaded gun is often faster than reloading.) Use it to turn away attackers. Just be prepared with something else when/if it fails.