A good discussion topic. I think your question misses the point a bit. The number of people praying makes no difference. God answers every prayer, no
matter who is praying (“righteous” or “unrighteous”) or how many it comes from. Sometimes, the answer is “yes.” Sometimes, the answer is “no.” The point of Abraham’s “negotiation” with God concerning Sodom and Gomorrah is not that God changes his mind. How can an omniscient being change His mind? Instead, God was demonstrating His mercy and the depravity of Sodom and Gomorrah to Abraham by this exercise.
I would refrain from looking to the televangelists for insight into the “underpinning of this widespread religious locution.” These guys very often
advocate a success-oriented faith (i.e., only by becoming a Christian and sending me money will all your financial and worldly dreams come true). The Bible is quite realistic about the prospects for persecution and suffering that lie in store for those who believe in God. Numerous examples are provided.
Instead, the answer is much simpler than that. We pray and ask others to pray because God told us to. Seek and you will find. Knock and the door will be opened. Even Christ, on the eve of his crucifixion prayed for this “cup to be taken away from him.” Yet, Christ also set the example by also petitioning “thy will be done.” God promises to hear and answer our prayers. The answer may not be the one we want or expect, but it is what is best for us. Why, because God promises that it will be.