The two derringers she’s holding are chambered in .22 Short. They through a 27-29gr bullets at about 700fps, enough for 6-8 inches of penetration in flesh. Due to the minimal sights, they can be aimed reliably only at a fairly short range, perhaps half-dozen steps. Reloading is done manually and isn’t very quick.
These guns can be used as offensive weapons, but even a medium-sized knife is likely to be more effective for killing somebody. A person threatened with one can likely escape being hit by running away. Despite the minimal power and range of these pistols, they are treated the same as a full-size .45 by the US authorities. In Russia, even people who can own 12ga shotguns — nearly 50 times more powerful — cannot own these for self-defense unless they are special people, friends of the government. Much the same situation obtains in New York City, where only special people get gun licenses and official permission to carry. Given that these are unsuitable to offensive use, why would they be as restricted as full-power sidearms?
Given the light weight and the small size, these can be easily concealed. Even an infirm defender can lift and fire them, providing a last-ditch option against criminals. A single shot of low power won’t likely cause a fatal injury, but we know from observation that most violent criminals flee as soon as the likelihood of any injury at all exceeds zero.
So the best guess is that restricting acquisition and carry of even the last potent firearms serves the purpose of keeping as much of the population as possible less safe from crime. Certain people — typically those who seek power of the public office — prefer their electorate to be less secure. The restrictions have nothing to do with public safety and much to do with retaining the official monopoly on force.
The woman in the photo is obviously not dressed for combat, and yet who would be willing to threaten her while she holds the two little pistols in her hands? A wheelchair-bound invalid is normally easy prey for thugs, but the vulnerability decreases a lot if the mere possibility of shooting back is introduced. The same is true for the aged, the slightly built and for everyone else who would normally be the natural fodder of the lawless. When you talk to anti-gun people, ask them if they would be OK with the weakest of the weak arms more freely available. If they aren’t, ask why not.