The purpose of prayer is not to overcome God's reluctance, but to help in yielding to His will. 'Prayer changes things' is only true if it conforms to God's will.
Jacob, though having a conniving spirit, nevertheless knew the superior value of the birthright, and struggled with everything he had to hang onto it.
Saul tried to placate God by massacring Gibeonites. Later, David yielded to the Gibeonites' by hanging Saul's descendants to avenge the slaughter. God was not pleased.
Millions lack faith to receive answers to their prayers. To a large extent, this is due to a lack of understanding what faith is.