If light travels at c, and the human nervous system is a lot slower than light speed, therefore it would take a lot of time for us to process what we see, why aren't we blind to what's going around us because everything we see is slowly processed at an inferior speed (let the inferior speed be defined as is less than c--the speed of light)?
I think you are confusing speed with rate. The speed of light is how long it take to for light to get from one point to another, not how often light "events" arrive at the eye.
To give an analogy, imagine a highway. There are 500 cars on that highway. They are traveling at 70 mph. Those cars then exit the highway onto a residential rode. They are then travelling at 30 mph. Does this require some of the cars disappear? No, they are all there, just moving at a different speed.
So for vision, imagine a certain light source emits a burst of 500 photons. The light source is 1 meter away from the eye, so it takes about 3 nanoseconds for the photons to arrive at the eye. Then they are converted into electrical impulses by the eye, and processed by the brain. Let's say this takes 100 milliseconds (I am just making that number up). That is about 30 million times longer. But it is still processing the same 500 photons, it just takes longer for them (or the electrical impulses they create) to get from one point to another.