I'll give you my take because it is slightly different. Your head generates oils, let's call them natural oils. When you wash hair first the "soap" takes effect which removed the smells, but also all of the oils. Then the other ingredients take effect. For nearly all cheap soaps these are silicone based things like dimethicone. Silicone based oils do make hair dry and lifeless longterm, at least from what I can tell.

The oils have a function, so if you are removing them, you probably should be replenishing them, with something that can serve a similar enough purpose. Unlikely to find a shampoo that can do both the soaping and the replenishing together.. they are literally contradictory effects.

So what you are left with is the realization that you shouldn't expect shampoo to replenish your hair, and have to think about what would do that properly.

If the shampoo is doing that wrong, then you are just left with soap, and a question as to the point of shampoo.