Airlines started checking for ID after the Unibomber made a threat at the LA airports for a 4 day period in the early 90's. When the threat was made, three things happened: 1)no mail was allowed into/out of these airports, 2)All air freight was diverted to other airports, and 3)all passengers were asked to produce valid ID. The airlines realized upwards of 15% of all passengers were flying with different names on their tickets. Some of the name differences were OK(John/William) but everyone else was forced to buy a new ticket. Over the four day period the airlines saw a big revenue jump from the LA Airports, so they decided to keep the ID rule in place.
Whenever an Airline asks for ID (on a domestic flight) for security reasons, I tell them you really mean for revenue enhancment---most of the time they just smile back.
I have flown domestic flights in many other countries (some with many more security concerns than the US)---not once have I been asked to produce any form of ID.