I don't have the link handy, but there was a great article arguing that the airlines could actually save more money not charging for checked bags because less people will try to cram their oversized luggage into the overheads, speeding up boarding times. Thus allowing for a lower rate of delayed takeoffs, which, over a long enough timeline, allows for more flights in a day they can charge for (and the added bonus of better customer retention).

If all the overhead compartments are full and they have to check your carry-on, they won't charge you any fee, at least on the major US airlines I've flown on.