Well, the reputation is an indicator of "how much does this user participate here, on a site about
For example, if my reputation on SO is 10 thousand points, on MSO 400 points, on SF 2000 points, and 101 on Cooking and on Gaming alike, it gives you a meaningful view of how much I'm active: mainly on SO, less on SF, sometimes I visit MSO and I've logged in at the Cooking site and the Gaming site.
With a single reputation, you might say, "oh look, a 10k Gaming user, he must be really passionate about gaming" - and you'd be completely wrong.
So, you can use the rep as a (very rough) measure of activity on that site, and that's its main purpose; making a all-site rep counter could be an ego booster for some, but I honestly can't think of another purpose for it.
Also, there's the matter of focus: I don't care about gardening, or conspiracy theories, or DIY projects, or latex, or LaTeX - and thus, making me click through pages and pages of categories to get to the Q&A about programming 1) requires thinking (bad for UX) and 2) wastes my time (what are all those categories, Yahoo's front page from 1998?). If the stackexchange dialog (top left) was the main entry to stackoverflow.com, I'd lose interest, precisely because there are so many things I don't care about (a.k.a. "noise").