I think the problem is that the airline will have to reaccomodate the bump-ees somewhere. If their own flights for the rest of the day (or the next day, or the forseeable future) are all full, then they will eventually have to put them on another airline, quite probably paying something like full fare to do so. Consequently, they try to avoid bumping excessive numbers of passengers.

On a more limited basis, though, a number of airlines do allow their top-tier elite passengers to book full-fare tickets on otherwise sold-out flights.