Well one concept that might help to understand this idea a tiny little bit better: You only need two points to perfectly define a circle. Adding any more points to the circle won't tell you anything extra about the circle. Now if you know that a sine wave is just a circle drawn out over time... you are half way there. :) Maybe this animation will help to visualize this:http://www.rkm.com.au/ANIMATIONS/animation-sine-wave.html
As far as summing is concerned, remember that in a DAW that is sample accurate (and has proper automatic plugin delay compensation) all the samples on all the channels that you are summing are at exactly the same spot in time so when you add two sample values, timing (aka the number of sample per second aka sample rate) is irrelevant. What is important is the accuracy of each sample value. The accuracy is increased by increasing the bit depth.
More bits gives more accuracy. Higher sampling rates gives more bandwidth.
So why don't we use 256 bits and 384Khz? Because we only need to cater to what humans can actually hear. 24 bits gives us arround 144 dB of dynamic range and 44.1Khz gives us arround 20Khz bandwdith. That is enough to cover what human ears can perceive.
UnderTow