Theoretically it is counter productive for any parasite that relies on a host to complete its life cycle to kill its host. This is counterproductive. However when the environment allows for overpopulation of the parasite which in turn overburdens the host, death can occur. Even something as benign as tape worm or round worm, can eventually overwhelm a host taxing its resources and thus making it susceptible to secondary infections.
Personally, after reading several scientific papers/journals/write ups about parasitic diseases such as marine velvet and ich (mostly in the commercial fish industry some about it in the wild), I have come to one conclusion. All wild caught fish have been exposed to it and exposure leads to contamination. However, do not think for one moment that tank raised fish are immune to it, because they can still contract it in fish keeping facilities (especially if they use fresh sea water) and worse, most have 0 immunity to it because they are never exposed to it.
Ich and Velvet (as well as other parasitic diseases) are usually NOT fatal in the wild due to the massive water exchange that keeps the parasitic numbers down in any given area, the predators to the parasite (and yes there are ich and velvet predators because anything that consumes plankton will consume them) and the fact that fish who are less than health do not live long enough for the parasite to reach obscene numbers in their bodies and shed it at those higher numbers. Predation keeps the Typhoid Marys at bay.
And as someone else already mentioned (many someones in fact) water quality is a HUGE factor because it impacts the immune system of the fish. And almost all fish exposed to ich or velvet and live, will in fact develop an immune system response to it.
Our closed systems with careful environmental controls gives parasites a natural leg up and puts all fish, any fish, at a severe disadvantage when trying to fight off disease.
Of course this is mostly my opinion, based on anecdotal evidence and my interpretation of articles written on the subject.