Petition prayer seems nonsensical wrt a omniscient/omnipotent deity.
I wondered about that too once, but studying the Bible answered that one for me....
Humans have a tendency to say "I can do it myself" or "I want to do it my way" so God provided prayer as a gauge to see how much you rely on him, as opposed to relying on ourselves. This is because we were designed originally to be ruled by him, but it was never going to be forced. We were to look to our Maker for his advice on how to proceed with any decisions we had to make. If you follow God's advice rather then relying on your own wisdom, you can save yourself a lot of disappointment and heartache. He already knows what we need, but we don't.....the aftermath of making a bad choice can affect us for the rest of our lives.
However believers must get something out of it, else they wouldn't keep doing it.
I don't think there is a feeling quite like having a prayer answered in a way that you never thought of. If you know God and have a close and personal relationship with him, prayer is as natural as talking to your best friend.
When you ask advice, he points you to his word...and there it is. There is no problem that cannot be dealt with by implementing his laws and principles. The benefits are obvious.
I don't know if we should be knocking down prayer so much if there is a real psychological benefit to it. Prayer, the purpose of prayer is to support the mental health of the believer if nothing else.
Prayer supports spiritual health, which in turn supports both mental and physical health. It doesn't mean that you are immune to these problems, but you are often in a better position to deal with them if your faith is strong. You build faith like you build a house. You start with a firm foundation and then, one brick at a time, the structure takes shape until it becomes solid enough to withstand the most powerful storm.
You should never knock until you've tried it.