I sometimes think that ice-diving is thought of as an "add-on" to say, an AOW course. In one sense it could be... dive teams with tenders and limited penetration of 50' or so. These dives go on all over the place generally without serious consequences. I've seen so many cases of reg freeze-up on divers farting around on the underside of the ice, 25' from the hole, I wouldn't even guess at the number. When that happens, they rocket back to the hole, assisted by the tender, and everyone has a big laugh about it. Those divers are typically rec divers, with a single rig and maybe a pony or something.
Then there are the dives like Shoredvr mentioned above. I know/knew the guys involved in that accident to be highly skilled and expericenced divers, but I always though that that particular dive was nuts. The wreck is fairly deep (as ice-diving goes) and a long way from shore. It was every bit a cave dive, with the added stressors of near-freezing temperatures, decent current and crap vis often. It was a perfect example of a situation where if enough stuff goes wrong, even the very best divers can't overcome all of the problems and conclude the dive safely.