Some things are obvious, but only in retrospect. Some things are obvious when pointed out, but still merit being said.
Why bedika with a candle, such that it can even be better that searching for chametz in broad daylight?
I believe the answer is what it forces you to do, and thus empowers you to do.
With all the lights on, or with broad daylight, you see everything at once. As such, you might not have patience to look at each place carefully. You see it all, your eye sweeps over it, and does not see any chametz. And as such, you can miss something.
With a candle, only certain areas are lit at once. In order to see if there is chametz, you need to focus that light on a specific area, and focus your attention on that area, to the exclusion of all else -- which is easier, since you cannot really see anything else anyway. To get a sense that you have covered every area, you focus on one area and thus move on to the next small area, meticulously covering every spot. Searching effectively with a candle requires such process, and thus empowers it.
And of course, the homily is free to flow from here, casting this as careful introspection.