That is a lose-lose situation.
Over-qualified people tend to be unhappy with their jobs and it can show. It is unfulfilling for the employee and, the employer won't get that persons A-Game for very long.

There really does need to be more reliable labour market analysis available for kids just starting college or university. Atleast give them good data to make choices based on. Flooding a market with people qualified for something that offers little to no employment prospects helps no one at all.