Not "broken" so much as operating on wrong assumptions - the assumption that the number of pax on a flight a year ago is a reasonable approximation of the number that will fly this year that same day (adjusting for weekends and holidays).

The problem is not that airlines are giving away too many seats - it's that they're flying too many empty seats no matter what they do.

Airlines say they're going to cut flights.
Folks, they don't cut flights if the flights are anywhere near full! In that case, they'd start raising prices.

And yield management isn't going to solve the problem. The problem is, to quote Yogi Berra, "If people don't want to show up, you can't stop them." The airlines now see a need to "right-size" the planes to the number of PAX.

The occasional free ticket (what's the average, about 6% to 7% across the board?) isn't adversely affecting the bottom line - it would be, though, if people quit flying "their" airline because of the lack of a frequent flyer program and began basing their decisions solely on matters of convenience and price. The airlines would have to coax each passenger each day instead of having the "cushion" of loyalty to get folks to take their planes even if they cost a bit more, or departed at a less convenient time.

No, frequent flyer programs *make* money for airlines (even when you don't count the miles they sell to their "partners").