It's important because when you "grok" it, your mind is different than before you grokked. Garridan's comment (http://ask.slashdot.org/comments.pl?sid=3805139&cid=43874611) is right on: you'll "sharpen your skills in symbolic manipulation". Pushups and bicep curls and stretching aren't sports: athletes do those things to condition their bodies for the real sports where nary a pushup is involved.
Maybe the marketplace for the kind of job you want demands a CompSci degree in these tough years, but I know many developers from a few years back who don't have one. Question yourself: would you be better off getting certifications plus a 2-year diploma and a 2-year headstart in the job market rather than a 4-year degree? You might do just fine with job-oriented training on top of your aptitude and some experience.