I'm talking about longer-distance runs here, not about buying premium vs cheap cables. And there are definitely people who need more than 6 feet of cable.
Short cables tend to use thinner wire than longer ones, because it's more flexible, less expensive to produce, and the additional thickness just isn't necessary at short distances (especially in a digital signal). So, if you chain a bunch of 6-foot extension cables together, not only are you adding additional connections to the chain, you're using a gauge of wire that was not likely intended to carry the signal that far. Both of these factors can reduce the signal strength and allow high levels of noise onto the line.
And yes, ones and zeros can in fact get "fuzzy" when the signal is not strong enough to be easily separated from the noise, and the receiving end cannot properly interpret the bits being sent. Of course, this doesn't result in a fuzzy picture like it would in an analog signal, but you can see artifacts (generally sparkles) in the picture, or worse: no picture at all!