Thankyou for wording the question so well.
Let's split this hypothetical higher power into its two possible roles: creator, and intervenor.
A being which directly created the universe to a design would have to be more complex than the whole thing put together, and therefore be the most complex and unlikely thing in existence. Furthermore it would itself need an even more complex creator, and so on ad absurdum. If you assert that the creator has existed forever and needs no creator-creator, why can't the (less complex) universe be eternal and need no creator in the first place? Whatever constraints you put on the universe to necessitate a creator, you immediately have to break to allow a creator. It's just not a good explanation by any standard at all.
Now consider an interventionist entity, built with or into the universe. Strip away all the usual rules like omnipresence, omnipotence and omniscience, and we're left with a force which acts some of the time, succeeds some of the time and leaves the rest to physics. Far more plausible than an almighty Godhead.
It's possible, sure, but is it likely? Are there enough unexplained events in our lives to make us seriously think that some have no material explanation? Perhaps your life is full of incredible coincidences, through which you believe you are being guided. The trouble with coincidences is that we only notice the ones that happen; not the ones that don't.
Say you're walking down the street to the grocer and you bump into someone you went to school with 15 years ago, in another city. The chances of this event are incredibly small, so it seems like destiny that you two would meet again here.
The thing is, how many people were there at your school? How many other people do you know, and how many of them might you have bumped into today? What about a stranger wearing the exact same clothes as you? Or your childhood hero whom you've never spoken to? Could there be a car crash right next to where you're walking? Could bird droppings fall right in front of your face and ruin your shoes? Or a meteorite?
There are an infinite number of possible events which might happen to you at any time and which you would regard as coincidences, or serendipitous. The probability of each one is almost nothing, but the probability of all of them simultaneously NOT happening is just as small if not smaller. A large amount of coincidences is practically certain for anyone on this planet. Even if you seem to experience more coincidences than anyone else, remember that you're in a sample space of six billion people and some of them are bound to have a surplus. Today's mass media trumpets any unlikely event to the whole world and makes us feel like our world is saturated with the incredible.
When I see a coincidence, I remember how many other amazing things might be happening, but aren't. I don't need a higher power to explain anything. I just know that it's a big world with lots of people who live for a long time.
None of this disproves gods, of course. It just shows that a creator is unlikely and an intervenor is unnecessary. This doesn't bode well for any power which is both creator AND intervenor.
- SmartLX