As I was led to believe in my M&G and by someone “in the know” the CP letter wasn’t a guaranteed interview, just an amount of points on your application... If that put you over the threshold to get a call, you went into the “short stack” to be interviewed. However, once in that stack, your position in that stack is relative to everyone else, as in you don’t automatically go to the top.

Apparently the AirlineApps rec from the CP is weighed roughly same as a normal LOR, maybe worth a tad bit more. The letter sent directly to the hiring dept is the big one.