The sacrifice of the Mass in fact does teach the Faith.
Only incidentally:
”Marcel Lefebvre often recalled the four ends of the Sacrifice of the Mass: praise of God, thanksgiving (hence the name Eucharist), propitiation (or atonement) and impetration (or intercession). Unlike the modernists, he insists on the propitiatory aspect: God who has been offended is made propitious by His incarnate Son’s act of extreme charity in offering Himself on the cross. But he also loves to elaborate on the praise and glorification that the Mass procures for God.“
Doctrinal instruction is neither listed nor derivative of any of the four ends of Mass. and nobody argued it should be taught as such prior to the liturgical movement (which was one of the reasons for introducing the vulgar languages and the versus populum posture), for the very simple reason that the Mass is for God, and not the people.
It only “instructs” in an indirect way, via “lex orandi, lex credentials.”