Why ask in prayer?

When people ask me to pray for their intentions or when I promise people that I will pray for their intentions, there are times that I catch myself asking whether this prayer of petition is effective at all. Let me put it this way, if some people pray for rain while others pray for a sunny weather, what will God do? Grant the request of some, and in the process, risk the ire of the rejected party?
And besides, if God is The all-powerful, The all-knowing, etc. does he really need an enumeration of things He has to do to put the world aright?
In one of my lucid moments (or moments of revelation, as I call them), I was struck by the realization that when I pray for something, it's not God's heart that is converted, what is changed is my heart.
The more I pray about something, the more that thing or intention becomes present to me. I would say that in a way, prayer enlarges my heart.
When, for example, I pray for peace in the world, peace becomes the subject of my thoughts, and the more I pray, the more peace becomes a conviction or a criterion for my ideas, my attitudes and lifestyle.
When I pray for a person, the more that person becomes an object not only of my prayer, but of my thoughts and my actions as well.
God doesn't need my prayer of petition. I need it.

Praying for someone means being present both to God and to the person, attaining a perfect balance between these two loves. (G. Thibon)