First, I apologize for such a scattered post. I got too distracted to check it for clarity.
Well, I sure wouldn't depend on salt to kill bacteria or fungus, either. But that doesn't mean that the healing qualities of a warm salt water soak is mere wives' tale. (Not that I'm a natural remedy type, by the way.)
For closed swellings the osmotic features alone are beneficial. For wounds, the flushing action, heat, and salinity inhibit proliferation of bacteria. It reduces inflammation as well as helps debride and oxidize wounds. Especially those healing by secondary intention.
As for taking an NSAID and/or abx, that's great, but have their limits - you don't want to overuse them, and even with them, wounds benefit from localized therapy. And as for neosporin, aside from the sensitization, there are times you don't want to use ointments for obvious reasons.
Think episiotomies, hand, and foot wounds. Sitz baths and foot soaks with salts added are more effective than warm water alone. And when dressing and cleansing other wounds, saline (or boiled salt-water) compresses and even packing is recommended by wound care specialists. As are sitz baths with epsom salts. I don't think they'd rx them if it were mere wives' tale.