I have been line breeding fish for close to 3 decades.
I do it to increase color, change color, fix a strain to breed true buy breeding back to the original parent(not always possible with cichlids), to lengthen fis and change shape, etc.
Most of the work I have done and do is with livebearers. Much of that uses hybrid Xiphophorus crosses.
With cichlids it can take much longer as some fish take a year or more to be mature enough to show its adult coloration and be able to breed.
The analogy that led to F78 generations is not really line breeding but inbreeding. In that situation if sibling spawns do not have another fish from a different set of parents breed into the mix, then you will have very deformed fish occurring by the 8th generation. It is important to introduce new fish by the 4th generation. This prevents deformities from forming in most cases.
If fish are not being bred back to the parents that share the same trait that you like than you are not line breeding. The trait will not be fixed and will become a recessive gene that can be lost in future generations very easily. Line breeding for trait enhancement is a little more complex than just inbreeding generation after generation.
I am working on a set of 8th generation Firemouths now. I keep looking for more reflective blues and deeper reds. I also pic fish with black edges on the pectoral and caudal fins. This makes the fish have more of a WOW color factor. I breed grandchildren back to original males.(unless I see an exceptional young male, then I breed it back to the original female.)
After that the trait should breed true to future generations.
I keep logs on broods, size, count, and how many culls I keep. Usually only one or two out of every 100. Culling is the most important part of line breeding.
I say no to hybrids, yes to line bred.
Manipulated or not, my firemouths are all T.Meeki, not crosses. To me, that makes a difference.
There should be a separate class for LB if people want to keep the ACA "pure". i personally would prefer to see them in the show. If they are banned I won't have any fish to show and will be disappointed!