I see Mary more as a loving, protective mom than a role model. I am not sinless, nor a virgin, nor a mom, so apart from things like Mary saying “yes” to God, it is a bit difficult for me to see myself as emulating her. That’s not to say she isn’t wonderful and admirable, just that for a “role model” I would pick somebody with a more active, less family-oriented life. I can relate better to the Apostles going off to preach but relying on Mary as the mother figure to give them support and encouragement. I can also see myself as a child who turns to Mary with my fears and hopes or when I need protection or want to talk about my problems with a mother who is older and wiser than me.
It seems like men either relate to Mary as a mom figure, or else (especially in the case of some priests and male religious) they see her as the gracious, perfect lady for whom they can go off and be a “knight”. Like St. Maximilian and the Militia Immaculata. Or, as someone else said, married men can be encouraged to pray the rosary by their wives. I think that was how my dad got into saying the rosary a lot - he was a convert and my mom was really into saying the rosary, so he adopted the habit by following her lead.