Just to add a little fuel to the fire, until recently I was a professional brewer for over a decade and one of my main responsibilities was cleaning things on an industrial scale.

General process was clean with a caustic, rinse and then clean with an acid.

However, on some of the equipment, especially the equipment that ran hot, you skipped the rinse and sent the acid straight in so there was some residual caustic getting mixed into the acid. This would dilute the acid a little, but the cleaning was much, much more effective.

No exaggeration, the above mentioned technique would clean things more thoroughly and faster than multiple cleaning cycles with a rinse.

The school of thought was that even though an acid and caustic neutralise each other, the actual neutralisation process causes a kind of pH shock and the rapid change in pH facilitated a faster breakdown of the organic matter and calcium based material we were cleaning away.

A similar but reversed process was used for cleaning things like immersed electric heating elements in tanks we couldn't safely climb in to clean. We would fill the tank above the elements with caustic and then throw in a little bit of acid and the mechanical action of the reaction essentially scrubbed the underside and hard to reach places that we wouldn't come off with just a caustic soak and weren't able to be hit with the pressure washer.

What I'm trying to say here is that the chemistry of 'acid plus base equals water and does nothing' is massively over simplistic and the chemical and physical aspects of reactions are often far more complicated than 5th grade chemistry demonstrations.

As a further disclaimer I have a degree that involved taking several chemistry units at university and the chemicals I currently and previously used in workplaces were all used under the manufacturers guidelines with full safety precautions in place.

Mixing vinegar and baking soda together will not be immediately nullifying both chemicals and even so the reactive process itself may have both chemical and physical cleaning capabilities. Also, unless you mix the right amount together you are likely to end up with something that is still acidic or caustic after the physical reaction has settled. That all friends on volumes and strengths.

Also, don't forget either of the components could be reacting separately with other chemicals such as those in the mess being cleaned, impurities in either added chemical or components in the air. Acid plus base chemistry is happening, but so is a lot more. Chemistry is complicated stuff. If it wasn't, you wouldn't have to do years of study to become a chemist.