Conversely, it never says that Mary is the “mediatrix” between men and Jesus - ever.
But that's a silly game. The important thing isn't whether the exact word is there, but whether the meaning is.
To your point: Catholics are convinced that Christ is the only mediator between God and man, in these ways 1) only He is mediator by very nature, being both true God and true man. 2) Only His work is necessary, because without Him, there could be no salvation. 3) He depends on no one else for power.
Mary does not fit this description because: 1) Mary is only a creature 2) Her role was not necessary, in and of itself 3) Her whole ability to do anything depends entirely on God.
But there's another level of meanings for "Mediator," meanings which indicate not divine power, but human her cooperation with Christ's mediation.
God freely choose her to make her Mother of the God-man, the Redeemer--on behalf of the whole human race she consented to God's plan of salvation by proclaiming herself the handmaid of the Lord. Mary was associated with her Son by the free decision of the Father, not because He "needed" he cooperation but because he CHOSE her cooperation.
In only this sense could she be (humanly speaking) a cooperator in Christ's Mediation, and this is how Catholics use the word "Mediatrix": Mother of Our Redeemer.