Sigh back to where i started
Baking soda is an abrasive. Of course, It's a salt. When mixed with so much water, itdissolvesand becomes CO2 with some left over minerals. It's abrasive nature is what scours the dead skin off of your scalp making it healthier. It also removes oils. You can use baking soda to clean dirty pots and pans. It's not just the water and sponge that get oil and grease off of them. It's the abrasiveness of BS.
Sure, they don't sell BS as a cleaning agent directly. But why do you think that many cleaning products advertise using it? Why would toothpaste have it if it did not clean as well and scrub? Why would clothing detergent have it?
Your hair gets oily because the pH of your scalp and hair is too acidic. When you use BS, which is a base, the pH of your scalp raises and you stop producing as much oil.
Sure Vinegar can be used to clean too. But it is not the only cleaning part of the BS/ACV wash. While the BS raises your pH, the vinegar brings it back down to the correct range for a healthy scalp.