Nearly all persons in positions of authority and responsibility had to go through some sort of application and interview process to become finalists for their positions. Why is it that persons running for president of the United States, the most complicated office in the land, can run as Democrats or Republicans without the parties formally screening them?
The party that gives their name to candidates has a responsibility for the quality of those candidates.
A system that reviews education, experience, temperament, and personality would not limit the number of qualified candidates approved by the political parties. Following the reviews by the parties and the party conventions, the primary and general election process would determine the outcome as it does now.