Comet is an abrasive cleanser with bleach in it. It will scratch surfaces of stainless steel, china or ceramic dishes. I don’t even use it on porcelain or enamel appliances but substitute baking soda and/or vinegar.
For the most part, I agree that “soap is soap”, but some strong detergents, for example, would make for super-astringent shampoo.
And Comet™ has abrasive particles in it that make it way more than “soap”. Just like I wouldn’t like to use Lava™ soap as a facial cleaner, I don’t think I’d use it on anything that couldn’t stand up to the abrasion.