Most hatcheries use the fish that were born and raised in the hatchery because those are the fish that home to the hatchery water and capture facility. Some hatcheries and captive raise facilties do grab some wild fish and add them to the egg and milt pools. The reason they do this is because any time you select or limit the number of fish in a population that can spawn, you reduce the genetic diversity of the population. Genetic diversity is the "insurance" that wild fish have against unusual environmental conditions, ensuring that some fish will always survive to spawn.
The other problem with hatchery breeding is you eliminate the very strong natural selection that occurs on the spawning grounds. Competition among males for females, competition of females for the best spawning areas, timings of spawning and fry emergence, water temperatures and flows are all natural selection forces that shape the characteristics and genetics of wild salmon populations. If you eliminate these natural selection forces in a hatchery environment, the hatchery population will genetically drift away from the wild type and become domesticated.
BC hatcheries are well aware of these problems and try to keep the hatchery gene pools high with wild genes and clip their fish so they can be distinguished. But I doubt the large industrial hatcheries in Russia and Asia that dump billions of chum and pink fry into the ocean take that level of care; they are meat hatcheries. There are now more chum salmon in the north Pacific from their hatcheries than wild chum.