I have to disagree. Cowboy Bebop was an animated film noir, an animated John Woo kung fu action movie. Any other ending would have felt like cheating.
Film noir can't have a happy ending. The protagonist has to die or go to prison for the rest of his life. It's a form with rules as strictly circumscribed as Greek tragedy.
And like all film noir heroes he was too cool and too badass to live. I repeat, any other ending would have felt like a tacked-on Disney happily-ever-after ending and would have made me RAAAAAAAAAAAGE.
As a feat of storytelling it was the most beautiful and perfect thing I ever saw.