This Chaga was removed using a hatchet with little harm to the tree. The Chaga on the other hand isn't good news for birch.
Chaga growing on a Yellow Birch - YouTube
I have found chaga on a single birch tree not within a large stand but agree more host trees will increase the chance. Chaga isn't always hard as a rock but can be woody. The best chaga is a softer yellowish growth. Chaga will have a hard black outer crust, softer yellowish inside and yes a hard darker brown component. Some can have greater amounts of hard/woody material. Just depends. This Chaga cut easy with a Mora 746.