Would the world be a better place if only certain people were allowed to reproduce?

For example, if governments required people to be highly educated, over a certain IQ, no genetic diseases (including both carriers and people with disease), no or limited history of heart disease/cancer, no criminal history, athletically inclined, and financially stable. 
Obviously this would never happen but it would certainly solve overpopulation and would potentially eliminate or reduce the occurrence of certain diseases. 

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