Exactly, just look what happened with dog breeding and how many breeds now suffer from significant genetic defects due to trying to breed desired traits.
The defects are largely a result of the limited capabilities of the breeding process (cross animals with a trait, hope that not too much other stuff comes along for the ride).
A fun angle: genetic engineering will eventually enable us to correct many of the problems in purebred animals. They are often good targets for even a limited genetic engineering capability (where the pure bred population has a high frequency of a single defective gene).
Some of the problems with dog breeding are due to the inefficiency of he breeding process, but others are simply the direct biomechanical consequences of the desired traits; for example the neotenous compressed faces of many lapdog breeds have consequences for mastication, respiration, and orbit shape that can't really be addressed without relaxing our selection for that particular look or accepting other tradeoffs.
A fun angle: genetic engineering will eventually enable us to correct many of the problems in purebred animals. They are often good targets for even a limited genetic engineering capability (where the pure bred population has a high frequency of a single defective gene).