In 2 Samuel 6, as the ark was brought back from the Philistines, David, knowing he was unworthy, asks, “How can the ark of the Lord come to me?” Just as when Mary visits Elisabeth, who responds, “Why is this granted to me that the mother of my Lord should come to me?” 1/4
So, first of all, scripture does not liken Mary to the Ark, the alleged typological references are basically all pretty obvious errors, some from excessive dependence on Latin.
Second, if she were the Ark, her virginity would be insufficient. You'd also need to assume she never touched anyone. Maybe some Catholics believe this, but it's clearly crazy since we know she had an actual social life (e.g. attending wedding at Canada, etc), and that sometimes involves human contact.
The Ark metaphor, moreover, is a late addition: the earliest uses of the Ark metaphor ascribe it to Jesus' incarnate body rather than Mary.