The trouble is keeping on focus for more than a generation.
(You may be thinking about the Methuselah's Children "future history" of Robert Heinlein, where he suggests a very rich eccentric with a short lifespan endows an institute to pay couples with long-lived grandparents to marry/breed, resulting in people with exceptional lifespans.)
The downside is what one generation may consider acceptable behaviour is not acceptable a generation later - Hitler's racial purity efforts, or the early 20th century drive to sterilize the "defective".
Plus, there's the timeline. It takes so many generations - Jared Diamond, in comments about agriculture, mentions that the life cycle of trees was too long for many to be domesticated by breeding; most are still cultivated to produce usable fruit with grafts. Similarly, IIRC reading once, there are no dometicated elephants; they are captured wild, usually young, and trained. Unlike real domestic animals, the breeding times are too long for them to have been selectively bred for tasks.
I guess the other question would be - what traits? And, who says that your "breeding stock" is going to cooperate, when even the guards are tempted to make an off-plan contribution, and the people in charge of the plan are certainly going to be tempted by the opportunity to make an off-plan contribution to the gene pool?
Sure, the nazis dabbled in eugenics but they only lasted a generation.
I think the closest thing you'd get to this would be the royal families. And that would be a very loose definition of selective breeding since they weren't breeding for a trait or traits, but for connections.
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