Traditional soaps are usually pretty irritating because they have a high pH (alkaline) and disrupt the skin's acid mantle. The modern stuff isn't called soap (e.g. cleansing bars) because they are made from synthetic detergents and are designed to have a lower pH and be less harsh. Trad soaps are also really good at removing stuff from the skin - including your body's own oils.

IME water + friction is usually enough to get skin clean and you get to keep your skin's biome intact. I've been waiting years for more skin biome products to hit the market, but it's not really happening. The dream is we populate our skin with microbes that consume the ammonia and other stuff we emit from sweat glands without producing foul odors.

Good to know