See this is all well and good.
But none of your reasons given are the main reasons put forward by those that advocate prayer.
I've read books on prayer, like "Don't just stand there, pray something" and they come from the position that if a church gets together and prays, healing can happen, problems can be solved, etc... etc...
A majority of Christians hold this view of prayer.
But the data shows that this is simply not true. Even if you see the value of prayer as meditation or a way to get closer to your imaginary friend, you still have to admit that the way the vast majority of religious people see prayer is wrong.
http://www.amazon.com/Dont-Just-Sta...=dp_db_cm_cr_acr_txt?ie=UTF8&showViewpoints=1
Read those reviews put forward by Christians who have read that book on prayer. They say things like:
"I happened on this book when I was dealing with a particularly bad patch in my life and it gave me the courage to pray and have faith that things can change, and they did!."
Or they go on about the power of being a prayer warrior and the effectiveness of intercessory prayer.
But the fact is, praying doesn't change anything in anyones life any more than not praying does.
That book specifically gives examples of how prayer solved money problems for the church. How prayer helped people get well. Etc...
And these are the views of prayer held by so many. And they are wrong.