I don't think people think of it like that. People are encouraged to pray for two reasons - Firstly, as a means to establish communication with the divine and build a relationship, whether one similar to father and child or one similar to friendship. Some nuns even go so far as to claim their relationship to Jesus may be likened to marriage. Secondly, as a form of petition, a plea for aid. The problem is, as you say, that there is little theological sense behind this second one.
My argument is that people don't really care about the theological implications. Throughout their lives, they have been encouraged to build a relationship with God. A natural facet of any such relationship is that of obligation - a father is obliged to help his child, a friend their friend. Their prayers do not go to the Almighty, who will measure their pleas on a silver scale and find them wanting. Their prayers go to the being whom they love, and whose love they feel assured of in return.
Indeed, people don't think of God as a magical sky fairy who will indulge their whims. They think of him as a friend or father who loves and wants the best for them... and when calamity strikes, a genuine friend would say 'screw it' to their own plans, no matter the consequences, and help.
In other words, prayer in such cases is an emotional outpouring - one which seeks reciprocation. It is not a rational or logical action in which people consider theology or, indeed, logic.