Shampoo gave me nasty, itchy sores on my scalp; I've tried all kinds, and nothing works well. As an experiment, I stopped using it about 3-4 weeks ago, and so far, my hair looks great, feels fine, and smells fine, as spouse confirms. For the first time in many years, my scalp does not itch.
I use soap mostly on my hands, or when something is actually dirty with something other than sweat. Otherwise, rinsing and scrubbing does me just fine. I also use deodorant, because when I don't, I reek.
I understand the knee-jerk reaction of "ew" to something unfamiliar -- I've had it myself to some threads on this forum -- but seriously, soap is not magic. Shampoo is not magic. Sometimes they're called for, and sometimes they're not.