Scientific selection would ignore age, weight, race, and so forth and would be less prejudicial. However, it is difficult to operationalize characteristics of good employees (responsibility, honesty, etc. ) which means a scientifically selected employee may have a lot of appropriate knowledge but not enough people skills or ethics.
The advantage is that is quickly separates the chaff from the wheat, based on research. The disadvantage is that it removes the possibility of potential from an employee who otherwise will be overlooked.
The mathematical analysis of the ideal employee is still dependent upon someone's view of a perfect employee. If the scientific criteria are illegal, such as preferences of a "perfect" employee based on gender or race or weight, it is still illegal. And a survey for analysis can be forged, filled in per what the subject thinks is right.
By using this method, you discount the human component, which is essential for workplace efficiency and compatibility. Also, tests can be lied on, but an in-person interview reveals a whole lot.