Why would good managers ever pass on opportunities to hire people with better qualifications than are required for a position? One reason is that some managers may fear that they are hiring people who, ultimately, might replace them. (Would you hire someone likely to replace you in the chain of command, or who is likely to compete with you for a promotion, thus becoming your boss?)
Perhaps an even more powerful explanation is that "overqualified" people are viewed as likely to move on to other, higher-paid positions as soon as one becomes available. Few new workers immediately operate at peak productivity; it takes time to become familiar with all the particulars of almost any job. If "overqualified" workers are viewed as less likely to stay, then employers may reasonably fear that they will not recover their costs from training a worker before the worker moves on. Thus, even superbly qualified people who are desperate and who would be willing to accept big pay cuts immediately may go jobless for very long periods.
People who lose positions because of corporate downsizing are not alone in being unable to find slots because they are overqualified. During recessions, many firms sharply pare back budgets for recruiting new hires from college campuses. And jobs below what a college graduate had hoped for but much above burger-flipper can be unavailable because of the "overqualified" label. During the 1990-1991 recession, many recent graduates seemed trapped in unsatisfying temporary jobs (e.g., as servers in restaurants). Only when conditions gradually improved during 1992-1994 did these educated but inexperienced workers begin to trickle into the entry-level career-track positions they had expected to find a year or two earlier.