While I think his music is usually good and occasionally great, I think the most interesting thing about Tom Waits as a person is the fact that he is trying to be cool. Between the sharkskin suits and the gravelly voice, he it seems like he wants to appear to appear that way (or at least well dressed.) While a lot of people are probably going to say "That's not that odd," consider that the majority of his audience (the indie rock fanbase) is based around authenticity, or at least the idea of it.
Stephen Malkmus and co. never really tried to be "true" slackers by being rough and rarely gigging; they just were and did. And Sebadoh didn't sing about being girlfriend-less losers who smoked tons of weed to be cool (talking about smoking weed is arguably cool but then again, Lou Barlow was never bragging about how dank his nug was); they really were chick-less potheads. But Tom Waits, like (The Boss, another musician who is not "indie" per se but is revered by the Pitchfork Media all the same), seemingly actively tries to create a persona and writes songs that are supposed to create a certain feeling. I think most people would agree that, say, Daniel Johnston writes songs to express his undoubtedly strong opinions and feelings. While Waits' music undeniably involves catharsis, it is in a structured, deliberate way.
But is this really a bad thing? While initially it seems that way, I think many people forget that music is essentially entertainment; Chuck Klosterman has noted that the job of a rock star is being cool. And if that's true, Waits is doing a hell of a job being both entertaining and at least somewhat authentic. Maybe he didn't get his gravelly voice by drinking his own urine but he seems like the kind of guy who knows a lot about train hopping.