If you keep an angler in a reef tank, you'll be pretty limited as to what you can keep with it:
Any fish that is smaller or up to twice the size of the angler will be on its menu and readily eaten.
Crustaceans = food as well.
Fish that browse and/or pick at rockwork will likely think the angler is a rock and stress it to death.
Those are the top three reasons. Another reason is that they really can't compete well with fast-movers for food (target feeding is a must). Additionally, they can't be fed too often or too large a meal (see "eats tankmates") as they have such a slow metabolism that the food will actually begin to decompose in their GI tract, resulting in bloating and death.
They're REALLY great fish, but IMHO/IME are best kept in a species tank.
HTH