I doubt they practice it much in 767s, though, despite the fact that they actually glide better. :)
What you of course do are power-off landings – on airfields, for example from the downwind, and simulated, i.e., you make a go-around just before landing, outside an airfield. Sometimes, it works, sometimes, it doesn't, there are many factors … that's why you actually fly with power idle and not with power off. There're still a few incidents, i.e., somehow the practice becomes tool real!
All in all, power-off landings and other emergency training are an important part of becoming a pilot but you don't spend that much time for them. Other things are much more time-consuming in a typical 45-hour syllabus.
You're thinking of https://en.wikipedia.org/wiki/United_Airlines_Flight_232
where so much of the plane broke that they had to invent a new way to fly it.
I can't turn up a reference right now, but like you say, in the next few years that failure was repeatedly simulated, and all the simulated planes crashed.
(IIRC, Haynes declined to try his hand at any of the simulations, explaining that the one time when it really mattered was enough for him.)
Flight 232 is another very interesting story, for sure.
Slipping to lose altitude fast is a regularly trained maneuver for glider pilot.
Still an amazing feat to pull that landing.
Like, sure, Pearson had glider experience... but he applied that experience flawlessly in an aircraft with a brick-like glide ratio, landing with no slats or flaps, all the while losing control authority as the airspeed dropped and made the RAT less and less effective, with 69 human lives at stake. Holy shit.
For anyone who's interested, Wikipedia is full of these stories of disasters and near-disasters, and they make for interesting reading.