I agree with you that it is “the church of the living God, the pillar and bulwark of the truth.”
I think that it was Augustine that said that when there is the church there is Christ, and when there is Christ there is the Church.
Christ cannot be separated from His Body.
And so it is with Scripture. It cannot be separated from Christ which also means that it cannot be separated from His body the Church.
Scripture was never meant to be alone.