I think people get all up in arms over line/in breeding because they don't have a full understanding of what it actually is.
If you have two animals that have little to no flaws in their genes, you can breed mother to son, father to daughter, or brother to sister over and over and over again and unless you get a random mutation to pop up, you should theoretically never have any issues.
Problems arise in line breeding when a genetic defect/disease pops up. If you line breed in this case, you increase the chances of the offspring having that disease. It's long and complicated to write all that's behind it here, but I'm sure most of you have learned about punnett squares in middle and high school. However, line breeding can actually help you rid a line of those genetic defects because it often makes it easier to detect an offspring's genotype. Just because one or both parents might carry a trait does not mean the offspring will carry it, show it, or ever pass it along to their children.
Linebreeding or even inbreeding does not cause mutations or problems to arise in itself, it just increases the chances of them showing up in offspring. However, the point at which this actually becomes an issue is after multiple (and I mean quite a few) inbred generations.
So, in my opinion, this law is a very, very silly one. Line breeding should not cause any issues in an adequate breeding program, and it's benefits go way beyond cost effectiveness. (And if you think about it, almost everyone in the world is a porduct of line/inbreeding of some form or another, whether you believe in Adam and Eve or evolution!)