Very very often human beings have to make decisions based on incomplete data. If it had turned out that antibiotics in soap saved lives what would we be saying if the industry that had waited years for iron clad proof before taking the relatively inexpensive step of putting it in?
Since the actual chemistry is over most people's heads, the "blue crystals" are where they invest all the magic that makes it work just like the ads claim it will.
Soap is pretty antibacterial by itself. ... and now I wonder if we'll next see a wave of soaps containing various reactive nanoparticles what whatever potentially not healthy stuff they'll use to address the fact that the public thinks it wants to buy something that is antibacterial.
Same thing there, it had probably just entered shared knowledge, it sounded sciency and natural at the same time, so why not add it to toothpaste? It must be good, right?
Completely worthless, pure marketing gimmick, yet people bought it.