The biggest advantage of a pistol caliber carbine in a SHTF situation is commonality of ammo and mags, i.e. greatly simplified logistics. Grabbing a sidearm and a rifle generally means that while you are better armed, that status only exists while two complete weapons systems and ammo supplies are functional. Run out of .223, you've got a plastic club. Mags get damaged or crushed, ditto (at minimum your ability to sustain volume of fire is impacted). Problem with the gun that you can't immediately resolve, you've got a plastic club and X lbs. of (for you, at that point in time) useless .223 ammo.
With a pistol caliber carbine, you do give up range and power, but you gain redundancy (especially with matching mags, or a revolver/lever gun combo), which is critical in an emergency situation with uncertainty as to when/if you can refresh your supplies and equipment. All your guns fire the same ammo, so as long as you've got a single round, you're still in the fight. Mags get damaged or crushed; oh well, you can still use the ones from your sidearm. And since they're interchangeable, you can carry less. Instead of 6 or 7 for the rifle and another 5 or 6 for the sidearm, maybe you carry 8 total, and throw them down whichever pipe is appropriate for the situation. Problem with the gun that you can't immediately resolve, all you ammo still works in the other.
Short of open combat, a pistol caliber carbine will do most things a person expects from a defensive weapon. After all, the .30 Carbine is a glorified pistol cartridge, and did fine in close combat. It won't help you in a 500 yard gun battle, but honestly in a SHTF situation it's extremely unlikely that I'm justified in engaging a target at that distance, and if I'm taking shots from 500 yards I can take cover or run. But to each his own, I have both and while I'd hate to leave my rifles, if I need to go now, I'm grabbing the XD , folding up the Sub2K and tossing it in the bag with 1,000 rounds and all my mags; move fast, travel light. It's not the weapon, it's the warrior; it's not the tool, it's the tactic.