Interesting questions, Adam. I have a lot of thoughts on the matter, but unfortunately I don't know of any hard facts!
Here are some things I have heard anecdotally. Aquatic caecilians are supposed to absolutely require soft water. Neurergus, as you mention, come from calcium carbonate areas, and it is "recommended" to keep them with limestone. (I suspect nobody has actually tested their tolerance though).
Certainly there are people who keep and breed a wide range of sal/newt species, both in hard and soft water areas. This would suggest that many species have a fairly wide tolerance, but again, I have no hard data. Certainly I was successful with several species, both in soft-water Virginia, and with continued success in hard-water New Mexico, where I've lived for the past 2 years.
In my own experience, I can tell you the following. After moving to a hard/alkaline water area, all my Notophthalmus died within 9 months. I am suspecting that the water at least played some role. I had kept this species succesfully for many years prior to the move. I have been very successful with Neurergus here, perhaps because they thrive in hard water. I know a couple of people who tried to adapt their Neurergus to aquatic conditions, only to see them die, and I suspect that soft-medium water MAY be to blame, but there's no way of knowing for sure.
One of the frustrations with captive care is that nobody really does "experiments". Any true experiment usually requires multiple tanks, a long period of time, and a willingness to risk the lives of some of the animals. Not many people are willing to undertake any of this.