This is not hard and fast gospel, but just my experiences... I had some brown flatworms in my refuguims, but have never seen one (Knock on wood) in my dispaly tank... I have three Mandarin's in my display...
When I got my newest Mandarin, she was a little on the skinny side (Okay, let's face it, she looked like a WWII Death camp refugee

) so I put her in one of my refuguims to fatten up on the copious pods in there. After a week or so in each of my refuguims, not only was she nice and plump, but I now can no longer find any flat worms at all...
No, I didn't actually see her eating any flat worms, but I had some in there before she was placed in there, and I don't now, and nothing else was added to the refuguims...
Also please note, I'm not advocating adding a Mandarin unless the rest of your tank can support one, as I'm sure you know they have specific non-standard requirements... And, I might just have had a fluke that liked flat worms, it might not be a common dietary habit of theirs...
As to why they're considered bad, they can multiple BIG time, to the point that your tank looks more like a glass|acrylic box full of moving flat worms. Not only is this unsightly, but they can smother corals that they're covering...