You're not hearing about the failures, so take that into account.
I've been fairly lucky with my attempts. I did have one gorgeous Coral Beauty that had been doing just fine in a 90 SPS reef with no nibbling issues. I got it from a friend and put it into my 58 gallon reef. It immediately began munching on everything in sight.
Angels are curious and will nibble on anything that appears like it might be food.
IMO, the real trick is to put them, (and every other fish) into a QT/Holding system separate from your display. Here, they can be watched for any signs of disease, and also conditioned to prepared foods. Once they are on prepared foods, you can fatten them up and ensure they are not "looking" for food.
This wont keep them from eating your favorite SPS or incredibly rare Blue People Eating Monster Miyagi Tort, but it should lessen the chances of it.
I've been very, very lucky with my Regal Angels. One thing I have noticed about both of them was that it took about a year for them to hit their stride and become more comfortable in my system and begin eating more aggressively and from a more varied diet.
I think all fish do this to some degree, but this is more pronounced in certain fish like the Regal Angel.
If you look at someone like John Coppolino, (Copps here), you'll see he has some incredibly rare and delicate angels in his systems, and he's had them for years. One of the things he attributes to his success is a solid QT/Holding system plan/protocol.
The thread starter, Michael Prater posted on another thread a great plan, (IMO) for angel/questionable fish QT. His plan is to tie a frag tank into his system and after the angel has been QT'd and acclimated to prepared foods, he intends to move the angel to the frag tank where he can see if there is anything the angel likes to munch on in a shallow-ish non aquascaped tank. IMO, this is a great idea simply because of the ability to remove the fish and find it a new home without having to go through the hassle of trying to catch the sucker from your display.
Nick