They're not core to the Alliance. The SC (ironically who you've named yourself after) are more loyal to the Kirin Tor than the Alliance, hence why the SC were not participants during the faction war in BfA. They honored the neutral position of the Kirin Tor. If they were core to the Alliance then they would have been active members of the Alliance during this faction war, alas they were not and thanks to BfA it is evident where their allegiances lie first and foremost.