The issue with "seeing" more satellites is frequency overlap where the same frequency range is used on the multiple satellites and the collection of more general noise. The overlapping signal from adjacent satellites will appear as noise and the collection of more general noise will reduce the signal to noise ratio, degrading and interfering with the signal that you want to receive.
Imagine having 5 radios all turned on at the same time and all tuned to different stations. Think how hard it would be to listen to all that mess. Going from what Brain said, imagine the above and you are trying to concentrate on one station to hear an important event, the other four would be noise to you and very annoying.