Um, no. The rules do not say that, at any rate. They do say that there are clerics who, rather than devote themselves to a particular deity, but "to a cause or source of divine power". Not *something*. There's nothing to suggest that a guy who believes the world was created by sentient bananas gains spellcasting abilities simply because he REALLY believes it. I mean, if you want your world to work that way, great, but that's not what the rules say.
They say that there exist sources of divine power besides the gods. That doesn't mean that anyone can make up any source of divine power anytime they like, just by wishing really hard.
Well, since the final call is up the the DM as to what qualifies as a cause or a source of divine power, you're right. But I like to encourage even wacky creativity, so I'm inclined to judge that if someone devoted themselves to advancing the word of their hand puppet, that's enough to qualify as a cause.
It's remarkably ambigious, and is left up to DM definition (as it should be, I feel). The rules don't forbid getting divine power from a handpuppet, as long as the DM sanctions that puppet as a source of divine power.
People will still see that some people's worldviews result in them getting free power, and some people's worldviews do not. This is different than anything that happens in our world, and it's unlikely that a world that demonstrates such behaviour would resemble ours. And I submit that such demonstrations of power will not supply the human need to believe in something greater than we can comprehend.
You're extrapolating based on the real world. This thread is about 10% rationalization based on the rules that exist, and about 30% speculation on what might be.
Of course it wouldn't resemble ours. That's like imagining aliens have the same definate 'intelligence' that humans do. Of course they won't. It's absurd to think that extraterrestrial life will even have eyes. But that doesn't make it easy to play an alien in a sci-fi RPG. It's like trying to analyze the psychology of elves. You can only go so far based on the loose information presented. I think speculation on the nature of religion, which isn't even in consensous as existing in the real world, could be usefully applied to a fantasy world.

Find out what you want, make sure it makes sense, and that's about all ya need, right?
People will still see that some people's worldviews result in them getting free power, and some people's worldviews do not.
Doesn't it require training to develop the rituals needed to summon divine energy for a mere instant? Or is it truly free to you? Because it doesn't have to be that way, and I think you'll find some of the problems evaporating if it's not. These are areas that the rules don't codify, only suggest, so there's lots of room for interpretation. But the world seems to make more sense if it requires as much training to summon the healing powers of the gods for a mere instant, rather than being "huh, my hands glow and heal wounds, ain't that a kick in the pants?"
If we go by the rules, there is no effort involved (except for the fact that there's nothing else you can do). If you want to extrapolate from the rules, for either physical actions (save for movement) or for spell casting, that's fine; but it isn't in the books.
Yup, it's extrapolation based on what the rules suggest. The rules suggest that spells are more than just things that happen with some fancy words. They suggest they're more than effortless. Or at least, there is nothing to suggest that they are any less effort than running 20 ft. in plate mail, as a for instance. If you'd like to suggest that running 20 ft. in plate mail is effortless because someone could do it all day without a penalty, go for it.

But I find the world makes more sense if you decide that spells aren't effortless...and it makes magic seem far less trivial. Trivial is OK, but it's hardly implied, just because you take no penalty for doing it.
There's no evidence to suggest that it takes any sort of effort, either. There is some kind of limit on casting spells that seems to come from nowhere - you can increase your spells per day by doing things like killing goblins, or sneaking back home past curfew, or winning the hand of Snow White. There's nothing to suggest that the number of spells you can cast per day is tied to anything except the number and difficulty of challenges you've faced in your life.
Challenges hone your body and your mind more than sitting in your room reading scrolls all day, in D&D. Higher levels mean you can handle more mental stress, and thus use more mental powers than those who have not endured such challenges. You simiply do not know mental pain until you've seen the horrors of a goblin up close. Until then, no matter how much you read in your tower, you are ignorant to the way the world truly works. Until you have lived life on the edge, you have never truly lived.
You only have the energy to harnass the divine powers a few times per day. No more -- your mind simply won't let you overwhelm it like that.
OR
I wave my hands and stuff happens. I got this power, mostly just 'cuz I really like the gods and believe in them and they like me. Need a cure? No sweat! The gods listen to me...at least, for a few times each day.
Both are valid interpretations of the rules as written. Which one you prefer is largely up to you. I think the world is more interesting with the first option, though. Miracles are not something that just happen with the twinkling of fingers, and to assume that spellcasting is effortless is to dismiss the hours of preparation and years of training that go into even harnassing the minor powers of the mind, the spirit, and the will.
You like the second better? Sure. But then, why don't the clerics heal every broken toe that comes to them? That question remains, if magic is effortless. It is dealt with if it is not.
