Digital vs Analog SNR
Spehro's comment is basically the answer. Imagine a link which subtracts a random, varying noise value between 0 and 0.5V from the input. You measure 4.5V at one end, but that could mean either a 4.5V input with no noise or 5V minus noise. You can't tell, and have lost your signal entirely.

With a digital signal varying between 5V and 0V over the same link, you can declare everything over 2.5V to be a '1', and lose no signal.