You are assuming that light comes in perfectly in spots, and that the purpose of vision is to replicate a "bitmap" of the incoming light. This would actually be very inefficient computationally.
In reality, vision relies on detecting salient features. Imagine a simple scene, maybe like this one:
Most of the white space of the wall is pretty uninteresting: you have no need to really process that information besides knowing it's one solid area. What is interesting in the image, if you are trying to understand the space your are occupying, is to see the edge between the floor and the wall. In fact, that's what really tells you this is a wall and a floor: if you only had the upper 1/4 of the image, you would just have a white box: you wouldn't know if this is a floor, a wall, a ceiling, the paint on someones car. The edge between the floor and wall gives you the needed context.
Lets think about how center-surround organization would respond to this image. In the whole blank white space, white light is hitting both the center and the surround: these cancel and there is little response. However, imagine what happens for an on-center off-surround cell right at the edge with the floor. That cell is getting white at its on-center, but only on about half of it's off-surround: the other half of the off-surround instead gets the darker wood floor. This cell would therefore respond to the imbalance in the average surround vs average center!
You can then combine many of this circular receptive fields to detect straight edges, like this:
Note: the LGN (thalamus) receptive fields are very similar to the retinal ganglion cell receptive fields. In V1, primary visual cortex, these receptive fields are added together to make "simple cells" which respond to edges.
I think this picture comes closest to answering your question about how overlapping receptive fields can be useful.
This image from the Wikipedia page on receptive fields shows what you get when you put a scene through a center-surround filter: note how all the edges are emphasized!
Other benefits: this type of detector works well over a range of light levels, for example different steps of gray will appear the same, even though the pixel intensity varies a lot. This way, you get similar responses to edges in both a dark and light room. These detectors also help to sharpen images. Note that computer vision uses some of these same strategies as well!
What if you wanted to detect spots of dark instead of spots of light? We often think of eyes as being "light detectors" but they are just as appropriately described as "dark detectors." Imagine you are a rodent looking up at the sky, for example: an important, salient stimulus for you might be a dark spot where a hawk is blocking light from the sky. Therefore, having an off-center, on-surround type of cell is just as useful as the opposite (and indeed, the retina contains both types of retinal ganglion cells).