I think some of the angler species fit what your looking for pretty well! Perhaps the sargassum fish? There's quite a few different kinds of anglers to choose from and they can all eat things very close to their own size (not recommended- but they can). Leaf scorpion fish are also really cool, rhinopias are bizarre- plenty of options to choose from. And although there are higher nutrient levels that need to be managed in a predator tank all the ones I've suggest or safe with corals (other than possibly sitting on them to long).
Also to answer your question- they're really isn't one answer. People like the oddballs for a bunch of different reasons. I like them because I'm fascinated by evolution and how the race for survival has pushed animals to the extreme in both forum and function. Some people like the under dog aspect of it as well and it's well documented that some things are so ugly they become cute.
For instance my mother loves her Product of Unknown Genetics, better known as a Pug. I can't tell you why she likes them but I can say for certain its not for their intelligence, how quietly they sleep or how she has to clean their wrinkles... However it puts a smile on her face and thats all that matters to me so I just like the daily pug memes she sends me knowing she's happy in doing so.
PS: Before you show your mother how to use instagram, consider the consequences...