Quite often a hive is not failing because of genetics. It's failing because the queen was poorly raised (usually poorly fed during development) or poorly mated (bad weather or lack of drones during mating) or maybe even a lack of proper bacteria and yeasts living int he hive. If I think there are characteristics I like about the queen, I will often let them raise her daughter and see how she does.
But still, picking good stock is a good thing. Pick bees that have survived the winter and are surviving without treatments. Bees that are gentle and productive. Bees, in short, that have the characteristics you like and raise queens from that stock.
If you view your genetic selection as removing what you don't want, in other words requeening the poor or hot hives, and keeping what you do want, in other words, raising queens from all the good hives, then you don't narrow the pool too much and only where there is a reason.