I would hesitate to tell God what He can and cannot do..... indeed, I hesitate to use the word "can't" in any reference to God.
I don't see prayer as a mechanical sort of thing, as if God is a waiter and we're ordering off some self-made menu. I'm NOT saying He can't or won't (see above), and I'm NOT saying it's wrong for us to pray for very specific things (even luxuries we actually don't need). I just don't see prayer as such a mechanical thing.
I think of prayer as talking with God. And that includes sharing what's in my heart/soul/mind. And yes, sometimes that includes material/physical stuff. Heck, I've prayed to God as test papers were being passed out (who hasn't?) and as I waited in the Dentist office (who hasn't?). Is that WRONG? IMO - no. God is our Abba and He cares about what is in our heart (and yes, He already KNOWS - so this isn't about informing Him, it's about SHARING with Him). It's relational.
God promises to "hear." And in a sense, to answer. But again, it's relational rather than mechanical. God is not an ATM machine, He is our Abba. If I pray, "God give me a Lamborghini Aventador" Well, what's behind that? What's in my heart/soul that is causing me to request that? God knows.... even if we don't. And I think it's often the need in our heart that He addresses rather than the literal words on our lips (especially since we have NO IDEA what we actually want and need). God is not our pet who rolls over if we do demand; God is not some mindless/heartless Genie in a Bottle. God is our Abba..... we are His precious children.
Another point: One think I've personally learned about prayer is that God may well answer it NOT by changing the situation but by changing ME. Changing MY heart, MY spirit. I think this happens a lot. Pray for your neighbor and you just may find that you go over to your neighbor and do things for them......God answered the prayer by doing something in YOUR heart. God CAN change things but more importantly, God can change US... and I think He often begins with the one we see in the mirror.
- Josiah