The primary action that soap has for fighting bacteria is breaking down oils and making it easier for debris and bacteria to be removed. Less food for the bacteria, and faster removal.
Bacteria will be destroyed by this process, but that’s coincidental to why soap works and provides benefit.
It’s why we don’t tell people to wash their hands by squirting soap on them, spreading it around and then rinsing it off. The critical step is the mechanical action that facilitates removal of debris with running water.

Yes, soap is necessary for hand washing because we need to maximize bacteria removal after defecation or before preparing foods or medical activities.

In the context of bathing however, you don’t need to sterilize your torso. You will also be rinsing your body far longer than you’re typically going to be washing your hands, which when combined with scrubbing results in a clean torso.

I’m not one of those people who’s opposed to using soap or anything, but that’s not the same as recognizing that it’s possible to wash and be clean without it.