I once worked with Rod Couling, a gentleman who raised Tumbler pigeons. He was also appreciated fine horses.
One day, in passing, I mentioned that I thought it would be very cool to have partial ownership in a horse sired by Secretariat.
Rod's reply surprised me. "I would rather have a horse from the same cross."
Rod's thinking was formed by the fact that animal breeding does not always progress in the forward direction. The combination of Secretariat's sire and dame had the potential to combine very well. One cannot extrapolate that Secretariat's genetics would combine as favorably with any other mare.
Consider a box filled with a thousand small pyramids. Each face of the pyramid is painted. The faces of some pyramids are painted all the same colors. Other pyramids have different colors on different faces. Every time you shake the box the faces of a hundred different pyramids are visible. The best you can do is see three of the four faces. Often, you will only be able to see just one face. Bear in mind that there are multiple layers of pyramids that are not visible.
Every time you shake the box is a new generation. After you have shaken the box you can remove the pyramids that have colors you do not like. That is similar to culling individuals from the gene pool.
Scientific breeding has been defined as "Breed the best to the best and cull the rest."
But then you have to mix the contents of your box with somebody else's box and then you each get half the combined pyramids.
Progress can be very, very slow.