So; you pray TO her and ask her to pray 'the same thing' as you ask?
I don't ask for particular stuff, or very rarely. It's more like I'm saying, “Holy Trinity, Mary: I'm spending this time meaning to be with you, purposefully and consciously, and so-and-so is on my mind, as I know you know.”
As for why not just an “Ave Iesu,” why do we not ask Jesus for directions to the nearest Piggly Wiggly? Why do we ask for one another’s prayers? Why do we want to spend time with wise and good people? To me, praying a Rosary is partially, in some respects, not only spending time with Mary but praying with her, being with God with her.
“Prayer” is, as I said, a word with more than one meaning. It's more than asking for stuff. But twice now, when I have conducted campaigns of prayer for them, two people who said, angrily, that they were atheists have contacted me and said they had come to believe and were praying. That got my attention.
I don't like to say, “Prayer works,” or “Prayer is powerful.” To me it's like a beggar saying, “Begging works,” when I think the more important thing is the generosity of his donors. But I still pray.