On this basis prayer sounds like meditation with some unnecessary theistic stuff thrown on top.
That's almost exactly what it is. "Prayer" is talking to oneself - there is nobody else listening. But the meditative process and self-reflection, verbalizing mistakes and goals, has its own value. Psychiatrists and self-help gurus will often tell people to do essentially the same things.
The problem of prayer is that people actually believe that it's some sort of conversation...or worse, a magic spell that will actually directly affect the world simply by making the request. I could pray for my uncle all day long, and he would still have died from his lung cancer. I will not win the lottery through prayer. Heartfelt words to imaginary friends will not land me a better job.
But I still meditate on occasion. And it would be more mentally healthy if I were to spend more time in peaceful self-reflection, identifying the mistakes I've made, anything I should feel guilty for, absolving myself or resolving to make amends, and clarifying my personal goals through verbalization. Those things all have their own intrinsic value.
“The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.” - Francis Bacon
"There are two novels that can change a bookish fourteen-year old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs." - John Rogers
“A world that can be explained even with bad reasons is a familiar world. But, on the other hand, in a universe suddenly divested of illusions and lights, man feels an alien, a stranger. His exile is without remedy since he is deprived of the memory of a lost home or the hope of a promised land. This divorce between man and his life, the actor and his setting, is properly the feeling of absurdity.” – Albert Camus
"...the pious hope that by combining numerous little turds of variously tainted data, one can obtain a valuable result; but in fact, the outcome is merely a larger than average pile of shit." - Barash, David 1995...
"Many that live deserve death. And some die that deserve life. Can you give it to them? Then be not too eager to deal out death in the name of justice, fearing for your own safety. Even the wise cannot see all ends." - Gandalf, J. R. R. Tolkien: The Lord Of the Rings