So you've lost that piece of paper with your friend's cell phone number on it. Why isn't there a cell-phone directory where you can just look it up?
Because the owner of the cell phone would have to pay for every call made to the cell phone by everyone who could get his or her hands on the phone number. The United States is perhaps unique in the world (OK, Explainer couldn't find out if it really and truly is sui generis, so sue me) in that we pay for both incoming and outgoing calls. In the rest of the world, if you call someone's cell phone, you pay for placing the call. When the U.S. system was put in place in the 1980s, wireless companies decided not to make people's cell phone numbers publicly available in order to keep their customers from having to pay for unwanted calls from telemarketers, ex-spouses, etc.
Explainer thanks Travis Larson of the Cellular Telecommunications and Internet Association. For whether cell phones are cheaper than regular phones, see this Explainer.