“They ask her to pray for them at the hour of their death, although, what exactly they are hoping to accomplish is not clear.”
Really? Unclear? We ask Mary, the Mother of God, to pray for us so that we may be made worthy of Heaven. Now that you know, does that bother you?
See http://www.freerepublic.com/focus/religion/2500255/posts?page=1
The prayer you seem to object to is one of the most ancient, common Christian prayers, it is NOT just the Catholic community that prays for the intercession of the Mother of God, it is the vast majority of ALL of Christendom, the Universal Church and most of the separated brethren.
The only one capable of making us worthy of heaven is Jesus Himself, the one who died for us in our place and to whom we go for forgiveness.
Mary has no more power to do anything to help someone get into heaven than anyone else on the planet.
Besides, God is very clear in the Bible that we are not to be trying to contact the dead.
Deuteronomy 18:10-12 10 Let no one be found among you who sacrifices his son or daughter in the fire, who practices divination or sorcery, interprets omens, engages in witchcraft, 11 or casts spells, or who is a medium or spiritist or who consults the dead.