I have bleached blonde hair so it's pretty dry. But my natural hair was very greasy. I've heard washing with just conditioner makes hair softer and less frizzy. It totally does! But once I have some growth by my roots I can't go more than 2-3 days without shampoo because I get greasy roots :(
Most shampoo are Alkali - sodium salt of LAB or any other synthetic emulsifier. Some premium brands use Potassium salt - just like washing soap and toilet soap. Potassium based shampoos are milder to skin, but conditioner is still milder form of the same thing. It is Ammonium salt. If you have very sensitive skin or scalp, you can use simply conditioner - it will work almost like shampoo. Basic Organic chain is the same, it differ only in type of salt.