"What about electric guitars?" you may legitimately ask. "We do ALL kinds of things to an electric's sound; why not the same for the acoustic?"
This is a good point. And if you're really looking for some freaky acoustic guitar tones, going through some outrageous processing is a good place to start. But if you're looking to capture the clean, natural essence of your guitar, then lots of processing will interfere rather than help. Except for some reverbs and delays, the tools most commonly used to alter an electric guitar's sound usually don't work well with acoustics (i.e., distortion, flanging, pitch shifting, extreme compression, drastic EQ settings).
Why not? Why do these work sound cool on electrics but not on acoustics? Well, when you think about it, the sound coming out of your electric guitar is already colored by all sorts of things; it's supposed to be colored! Your choice of preamp, effects, speakers, and such can either anonymize your guitar (the Scholz Rockman can make even a cheap guitar sound like part of the Boston guitar army), or turn its liabilities into a really unique sound (the 60-cycle hum coming off of your Sears guitar just might be the sound you want for your new hit single). But an acoustic guitar is almost always recorded clean; the goal in recording an acoustic is to have a minimum of coloration from the microphone (assuming that you're micing the instrument). That means that the sound coming out of the wood has to be top-notch. While there are exceptions, the best place to start looking for one of these beauties is in the upper price range.
What it boils down to, then is that the closer you look at an instrument's "pure" sound, the better of a starting product you're going to want to have. The fact that there are fewer elements in the chain of sound from the instrument to the recording means that each element of that chain will have to be as high in quality as possible. The differences between the mediocre and the superior instruments will become PAINFULLY obvious. For instance, generally speaking, both a Volkswagen Bug and a Porsche 958 are "cars"; but the closer you look (i.e., higher standard of measure), the more differences you're going to notice. Same in the studio. The higher fidelity recording and performing environments are going to WANT a great guitar as a source. There are exceptions, of course, but generally speaking, a cheap instrument will have every bit as much trouble measuring up to a great one as that VW Bug will have trouble matching the performance of the Porsche. Sad, but true.