Changeup, you have a couple of things wrong. Physical traits are generally inherited, and though rare can be influenced by outside factors. Exposure to heavy metals in the womb can nullify any inherited genetic traits, as can exposure to chemicals, gases etc... Also in order for your examples of athletes and their offspring, you forget that the mother has to have similar traits in order for the examples you use to be true by genetics alone...otherwise social environment is the dominating factor. Obviously a child with a birth defect will not be able to follow in it's parents footsteps, but then neither would a child of star athletes if that child was never exposed to the training that builds the necessary skills.
Good hand to eye coordination can be an inherited trait but it can also be learned. Through training and repetitive motion, people build muscle memory. Their brains memorize the motion that the eyes see, then register that to the nervous system and tells the body what muscles to activate in response to that input. The more times that motion is repeated the faster the response can get assuming nothing else is thrown in the mix. Take a look at Bruce Lee, nothing particularly outstanding in his genetics or upbringing. He became what he was as an adult by constant repetitive training and understanding of his body.
The SEAL program pushes the mental and physical limits of individuals to extremes beyond basic training, but it cannot overcome the deep rooted fight or flight instincts that people have. When those people (Navy and Marines) enter the program they all know that at any time they have the choice to stop training. The only way they could lower the the atrition rate would be to remove that choice, then only the most resilient would enter the program to begin with and the starting number of candidates would be much lower.
What you're seeing on television, is not the extent of what really happens in the SEAL program. There are a lot of reasons for the atrition rate and injuries account for a large portion of it.