Well, from what has always been my traditional filter of looking at the world, it just is illogical. If God created the world, and had all 3 of these powers, the world would be perfect, both God and humans would be fulfilled with what they required out of the world, and if God found worship of him so important, then he would make it obvious that he exists (and would be perfectly capable of it).
*Nod* I can see that as a personal belief - I think it makes sense from your point of view as well. Me, I tilt that just a little bit. In my belief, I think we did have perfection, once, but mankind wasn't ready for it. So why didn't God create us perfect so we could enjoy paradise? Well...my answer would be this: I can't know perfection unless I have something imperfect to compare it to. And if I'm not ready to enjoy it, why have it?
In my opinion, I don't think God needs us. If you're omnipotent, perfect, and fulfilled in yourself you don't need anything else. So maybe the question becomes why create anything at all? Why create creatures with rational thought with the ability to reject you and reject each other? Why set yourself up for that heartbreak?
That, to me, is the real question.
But humans are attracted and drawn to the mysteries of the universe and they're drawn to understanding what created what - and why. And how.
Logically, Duty, you're right: It's difficult - perhaps impossible - to measure concepts beyond the five senses. But there are too many things that can't be quantifiable, can't be measured with human insight - there are things we can't understand right away because we just don't have all the knowledge yet. I'm not saying we won't have it, but...yeah. Sometimes bad things happen and we don't know why. Sometimes supposed holy men do really horrible, rotten things in the name of their gods. Sometimes followers of holy doctrines say and do horrible, rotten things. There just aren't good enough answers for those things.
But now I'm rambling - I'm being extremely INFJ and it's probably starting to irritate you.
I'll say this: Keep questioning. Keep asking. Eventually the answers will make sense.