There's actually no guarantee that wild fish aren't related either...in fact it's quite likely that wild fish are related in some cases. That doesn't mean that "related" fish are an issue.
There's widespread (mis) belief that wild fish are optimum in terms of color, "strength" and other characteristics that hobbyists desire and that such hobbyist-desired characteristics get "diluted" with each generation in captivity (F1 fish are less colorful than wild ones, F2 fish are less colorful than F1 ones, etc.).
This is, of course, nonsense. Some wild fish hold the characteristics desired by hobbyists. Most hold the characteristics desired by Mother Nature. And they might not be the same. Nature doesn't generally favor the largest, most gaudily-colored or long-finned. Or albino. Or veil-finned.
The point of Line breeding is to inbreed fish toward desired characteristics. Pick the reddest fish and breed it with the next generation of reddest fish, for example.
Can undesired characteristics emerge with line breeding? Sure. But fish inbreeding is different than, for example, human or mammal inbreeding. Especially with mouthbrooders / harem spawners there is generally enough genetic diversity in a group of fish to maintain lines without deformities or other issues for many generations. A couple of our speakers have covered this quite clearly: whether wild fish or F2000, just don't continue to breed fish that produce deformed or otherwise undesired offspring.
Unless the goal of the line breeding is deformed offspring
Where do you think lyre-tails and long fins and short bodied fish and "White Knights" and all the rest come from? Same with "koi" angelfish, bright orange discus, long finned bettas, koi that aren't brown carp, etc. Some people cull those fry. Others work with them to develop new "lines."
The issue of genetic diversity and "new blood" is also misunderstood. People seek to get "new blood" from different sources. But that fish that come from different hobbyists doesn't mean that they come from fish with different ancestors. It's not as if people are regularly importing fish from Lake Victoria or Honduras or Madagascar (or lots of places for that matter). Nor (for the reasons above) is it as important as some think. In the case of line breeding, adding new, "unrelated" fish is counterproductive.
Introducing "new fish" also introduces risk. It assumes that the fish involved are what someone says that they are...which isn't always the case. How well do people maintain provenance back to the wild of fish in the hobby? To ensure that fish are from consistent collection locations? Different imports? Generally not so much.
In the case of CARES fish, the goal should be to maintain as authentic as possible fish to wild populations. Easier said than done...but an important sub-goal of the CARES program should be just keeping these fish species available in the hobby. Also not an easy goal in many cases.
To me at least, line breeding and hybridization are closely related. The goal of both is to create something different than nature. The tools are slightly different. For example, while mixing fish from two different geographic populations of Aulanocara (peacocks) to get fish with desired characteristics from both is technically "line breeding." Two scientists could (and have) split them into two different species. Then it would be hybridization. Are fancy discus line bred or hybrids? Depends on whose version of taxonomy you support. Many we just don't know their actual origins (again, fancy discus). But, again, to me it really doesn't matter. The goal isn't to maintain something authentic to the wild.
The matter of morals and ethics of line bred fish and hybrids, etc. is not often enough rationally discussed. "Fancy" fish have been the foundation of the hobby since like 200 AD (colored carp) and represent some of the most popular fish in the hobby and industry. I just can't make moral bright lines between fancy line bred fish and fancy hybrids. Both can have deformities that harm the fish's health. And both can be tattooed or dyed (which is a whole different issue). There's room in the hobby for people who enjoy developing lines of "new" fish (not easy to do well!) and for people who maintain "authentic" fish. But I digress...
Matt