I am not so sure it is all that straight forward - vaccinating and no problems and not vaccinating, animals die. Most goat deaths are brought on by some kind of stress factor plus the original cause of infection, so generally healthy and unstressed goats have a much higher chance of surviving. I use Lambivac rather than Heptavac for the goats (and Heptavac for the sheep), thats after I read all the advice from the GVS.
Given the large number of people who keep their goats/sheep/dogs/cats/children unvaccinated and they live a full and long life the evidence is probably not clear cut. Also animals/people survived BEFORE vaccines became available.
I only ever got a tetanus jab when I was nearly 40 years old! (and I had been mucking round in forests/gardens/chemical laboratories etc for a while by then). But am not very good with needles, even though I can readily stick them into my animals, but not people nor have them stuck into me.