I wonder what people might think of an unconventional Catholic perspective on this, from the mystic Meister Eckhart:
"...When I pray for aught, my prayer goes for naught; when I pray for naught, I pray as I ought. When I am united with the God within which all beings exist whether past, present or future, they are all equally near and equally one; they are all in God and all in me. Then there’s no need to think of Henry or Conrad [he means of people to pray for, like Tom Dick and Harry as we would say]...
I ask, 'What is the prayer of a detached heart?' My answer is that detachment and purity cannot pray, for whoever prays wants God to grant him something, or else wants God to take something from him. But a detached heart desires nothing at all, nor has it anything it wants to get rid of. Therefore it is free of all prayers, or its prayer consists of nothing but being uniform with God. That is all its prayer...
When I pray for nothing, then I pray rightly, and that prayer is proper and powerful. But if anyone prays for anything else, he is praying to a false God...I never pray so well as when I pray for nothing and for nobody, not for Heinrich or Conrad. Those who pray truly pray to God in truth and spirit, that is to say, in the Holy Spirit...
People often say to me, 'Pray for me'. And I think, 'Why do you go out? Why do you not stay within yourself and draw on your own treasure? For you have the whole truth in its essence within you.' That we may thus truly stay within, that we may possess all truth immediately, without distinction, in true blessedness, may God help us..."
- Meister Eckhart (c. 1260 – c. 1327), Catholic mystic & Dominican priest
Seems like not all theists are even in agreement concerning this. Although as stated, Eckhart was a very radical and free-thinking theist, so he is hardly representative of the standard perspective on this.