Her perfume line brings in $2.5 billion in revenue. Her retail businesses bring in $4 billion in sales. That's on top of her music career, and being paid six figure sums just to show up at parties.
If she'd been sensible, I'm sure she could've gone off to Harvard or Wharton, taken over the family empire, and be sitting next to her vaguely-abusive father in a board meeting right now. But being a coked-out ditz is apparently very, very profitable, and has given her decades of staying power in the public consciousness.
That said, I do think it's harder to say if it was a conscious strategy (i.e. a publicity team sitting around saying, "Ok Paris, tonight you're going to throw a drink at Bill from TMZ, we've already set it up") vs the fact that one can be both a complete mess in some aspects of your life and well put-together in others. If the checks keep rolling in, and you're still having fun with it, I'm sure that "all publicity is good publicity" becomes a pretty reassuring mantra over time. Our obsession with Spectacle does the rest.
To draw a parallel: look at Elon Musk. He's built a personal brand around posting cringy memes on Twitter. Is he a moron? Possibly, in at least some senses. Has his public persona made him buckets of money and contributed to Tesla having a PE ratio that confuses the hell out of analysts? Undoubtedly. One's just targeted at twenty-something women who watch too much reality TV, and the other at twenty-something men who read too much Reddit.