1. Purple heart destroys tools. This stuff is hard as a rock. It blunts files and destroys sanding belts. It's also hard and slow to cut with a band saw.
2. It's almost impossible to use a belt sander on purple heart without creating burn marks. You have to use a brand new sanding belt and then only sand lightly, which doesn't do much good, because purple heart is so hard. And then it's hard to get those burn marks out.
3. It's hard to get a good finish on purple heart. You have to sand and sand and sand with your hand. Then sawdust gets in the grain and imperfections and looks nasty when you put a finish on it. It's very hard to get the tool marks out of it. Once you put a finish on it, these imperfections show up, and there'll be ugly brown spots on it.
4. Purple heart is brittle. Some people have made successful bows out of it, but it's more trouble than it's worth. It doesn't do well in compression, and it frets easily. (Frets or chysals are compression fractures that look like little lines running across the belly of the bow.) I would only use purple heart in handles where it doesn't bend.
Purple heart looks really good with Osage provided you can get it looking good. With patience, it is possible. Just sand with a rough grit a whole lot until you get all the tool marks out and get it nice and even. Then start sanding with finer grits. Once you finish sanding, wipe it down with acetone. That cleans out any saw dust that gets in the grain. I have a friend named Sam who does amazing things with purple heart. I just don't like using it myself.