If OTC cough and cold medicines don't really work for children why are they even sold?

Same reason... Homeopathic remedies and all-natural products are sold: they make the person who buys them feel like they are doing something positive. Don't knock it, they make parents feel better. If nothing else.
See below. There are a lot of otc medications, herbs, and supplements that are sold which have no specific benefit. It is all about profit for manufactures.