I like your description.
Twice I have seen guys shot with .25s, in neither case were they killed outright or even put unconscious, but it put both of them on the ground and in a very passive mood. They are, or at least used to be, a very common bar pistol.
At really close range, where accuracy is not a factor, the best bet is a single shot pistol that takes a shotgun shell.
There’s a reason a very old Baby Browning .25 ACP lives in my boot on a regular basis. No, it doesn’t do well at any sort of standoff range - but then, that’s not what John Browning designed it for. It’s designed for up close and very personal work - say, while you’re rolling around on the ground with an assailant. Draw .25, shove under the assailant’s chin/stick it up his nose/socket it into the guy’s ear/jam it into his eye and pull the trigger. He will NOT be getting up from that because, like the .22, that .25 will bounce around in the skull like a berzerk pinball. Failing that, just jam it up against the skull at any point and fire. The .25 *will* penetrate the cranial vault at contact range and while you won’t get the pinball effect, the guy *will* still go TILT. And it’s a centerfire cartridge, so it’s reliable (which a lot of people forget). Failing that, jam it into his ribs and start pulling the trigger as fast as you can. Either way, the assailant will not be very interested in continuing the engagement.
Is it a good primary carry caliber? No. You should have something better because beyond about 3-7 yards it’s a problematic stopper at best.
Is it better than nothing? Yes. In fact, I would even go so far as to state that it’s probably better than a knife for contact-range defensive use, as it’s more difficult for an assailant to get the little .25 away from you than it would be a knife and it doesn’t require significant strength to use.
Is it proven effective within it’s intended use as a contact-range weapon? Very. Generations of nurses have carried them and they have prevented many, many late-night rapes over the decades. In fact, I once showed an older friend who is a retired nurse the little Browning and she immediately lit up as if seeing an old friend again. She’d carried one in a garter belt for years when she worked the night shift in a hospital as did many of her co-workers; several had had to use theirs to prevent imminent rape (or worse) over the years, way back when.
At contact range, the .25 auto is hell on wheels for an unsuspecting assailant.