I think it's pretty tricky for people who do want it . . . so yes, it's even trickier for those who don't. If nothing else, it should never default to being ON. Although I can see value in allowing users to create a document preset that does default to pixel alignment. Nevertheless, until you need it, it should be something that's never experienced unexpectedly.
Web designs are so high-res these days that I rarely need it for the web. Mainly I use it for even less common projects involving small digital displays, portable device user interface design, etc. It's indispensable there, but definitely a rare use-case. Some textile design people apparently use it, too, or so I've heard.
Having it a live effect is interesting. I'm not sure how that would work.
The mangling you speak of, if I'm thinking of the same thing, does seem to be repairable by the realignment technique I just posted. Maybe there's something else it does that I haven't run into.
Vectors and pixel alignment are intrinsically at odds with each other, so I'm not sure there will ever be a really intuitive way of doing it. To my mind, I would expect that all anchors would be forced onto integer pixel positions when it's turned on, without any of the current weird compensation for stroke width. It would then be more obvious that the stroke itself needs its own alignment relative to the path.
In any case,the feature should, as you say, be active only when very explicitly needed.