It would actually be really cool if effects like that could happen. It'd make for a truly stupendous disaster, and therefore incredible Fun. It also fits into how the next release is trying to make the underground a bit more 'interesting'.
The current system where bodies of water tend to have silt and mud around them would allow it to be naturally stabilized, just waiting for some foolish person to make a reservoir for their fortress well and not realize part of it's salty stone, cue the entire fortress being undermined and ... well we'd actually need a more sophisticated cave-in system like in 2D DF for that to be a disaster, most likely you'd just end up with your fortress suspended above a salty underground lake. Which is cool, but not as Fun as it could possibly be.
In the case of that Louisiana lake that breached the mine, it sounds like it would've had lots of surface area where the fresh water from the drilling hole could flow against the salt walls thanks to the mining tunnels. So I wonder if a case where water was simply pressed against an undisturbed (non-hollow) salty rock wall would still cause rapid erosion. Maybe it would still happen, it would just take more time as the water slowly dissolved just the little bit of salt that it was able to get at.
I could imagine this being replicated in Dwarf Fortress, but the potential I see for FPS-killing is not just when you have a lot of flows going through your fortress, but that in such a situation you'd have hundreds of walls being destroyed at once. I usually notice a great deal of lag if I have several miners ramping out walls, or to a lesser extent if they're doing a lot of mining, so I wonder if hundreds of salt walls being dissolved at once would just kill a fort's FPS for hours on end.
The toughest part about having this in DF, I think, would be the potential for fortresses to get lagged to death without the user having any idea why. As an old-timer it seems worth it to me just for the Fun factor, but it could make things really tough on newbies.
Though I can't imagine it not being an Init option (Salt Erosion Yes/No), so that'd solve that problem. All that's left is all the bug-hunting and initial work to put it in.