I had a commercial goat dairy for a number of years. Through no fault of my own, I have had a LOT of experience with Johnes, CL, and CAE. I was able to eradicate both Johnes and CL from my herd without too much trouble. While I greatly reduced the rate of infection of CAE, I was never able to totally eliminate it.
Unpasteurized milk is not the only way CAE can be transmitted from one goat to another. Does can infect their newborn kids by cleaning them off after birth. Nose to nose contact between animals can spread it. If negative animals are exposed to the after-kidding discharges of a positive doe they can become infected. If you have both positive and negative animals, it is suggested they be housed separately and there be an alley of at least four feet between the positive and negative herds. In case you think I am nuts, for several years I participated in a clinical study of CAE conducted by UC Davis.
As for CL, it is not nearly as dire and hard to get rid of as people, including medical professionals, tell you it is. When I first started raising goats in the late 1960's it was very common. A lot of herds, including mine were infected with it. We all managed to eliminate it from our herds. If anyone is interested, just PM me and I can send you a paper telling you how we did it. It must have worked because we all managed to get rid of CL and it never came back. We did not find it necessary to cull positive animals either.