This is kind of an interesting idea---and a very limited genepool in the tank for something that has to reproduce within 2 months, and go on reproducing, with an increasing number of the fish developing some sort of resistance to their doing so---the same researcher, Burgess, has a paper indicating indeed there might be some resistance developed---would greatly diminish the number of hosts, while the gene pool was getting increasingly inbred, ergo more recessives coming out. And recessives are usually not the strongest traits to have. So---
Exactly what state of the art is now on the question I'm not sure, or whether Burgess is still at it--94 is a while ago. You'd think people would rush to research this ubiquitous pest, but money for grants goes where the money is, and this is a hobby.
Anyway, I've put out a query to some of our resident biologists to get their take on it, but one thing WOULD semi-logically follow from what Burgess is saying: namely that continually adding fish to your tank is reinforcing the gene pool of any ich in your tank.
There are two jokers in this deck: 1) some fish sources do their own quarantine, which leads some people into a false sense of security about not quarantining---and they'll get slammed the first time they buy from a non-safe source; and 2) some people who lose fish rush to replace them---again, without quarantining, sort of like that Roach Motel commercial: they check in but they don't check out. The dogged hobbyist sends in fish after fish after fish, and keeps losing them. MAYBE he's reinforcing the gene pool so well that he has really viable ich going on: a one year moratorium on new fish---easy for us old hands, but for a newbie over-excited and wanting to try every new fish short of a whale shark---disaster.
One might also suspect that the one place where, if no countermeasures are taken, ich strains could breed at will---is the local fish store.
This discussion and specifically this post is one of the best I have seen on Reef Central. I personally rarely introduce fish (no room, no deaths) and do believe the fewer fish introduced, even with a proper quarantine process in place, the better. I do not know about ich and eels so cannot offer much in that area but I think that hypo, carefully controlled, is the best way to go.
I do know that some fish develop resistance to ich after multiple exposures to it. I don't think we know why or at least I have not seen a scientifically based explanation.