From my understanding, except for a Daily and a bi weekly there isn't any rail connection between Banngalore and MAngalore, but I guess there would be a much larger demand. Coming to the point, SBC Kannur exp via mysore is taking the route as shown. whereas YPR - Karwar goes via tumkur, ariskere hassan.
But Why isn't there any train going through Kunigal and Shravanbelagola which is obviously the shortest path between the two major cities ? Does that line exist ? If it exists does it has anything to do with the HMRDC Agreement ?