This is very simple.
TREMENDOUSLY talented. Ahead of his time. His writing during the 1960s and most of the 1970s was groundbreaking, and even as his chemical usage was growing, he still had clarity of thought and purpose. I even liked The Curse of Lono (I have a relatively rare copy of the book), which was written around 1980.
And if HST only wrote his first 4 books, plus his articles in Rolling Stone, then I believe the quality of his production exceeds JD Salinger and is the equal of Ernest Hemingway, particularly in the impact on a generation of readers.
Did the booze and drugs have an impact on his diminishing returns? Yes. I think he became so enamored with what he accomplished in the 60s and 70s that it was almost like he had to live up to that, doing more and more extreme stuff.
But I also think that the election of Nixon and the disappearance of Oscar Zeta Acosta made him increasingly paranoid and isolated. And his fame made it harder and harder to do Gonzo journalism, because he was no longer some anonymous crank writer, he was a guy whose fame made it very hard for him to be as observational as he once was, even if his journalism was always participatory too.
To use a similarly-timed comparison, I would look to David Bowie. His first 10 albums from the late 1960s up through Low (recorded in 1976 but the record company delayed it until 1977) were amazing works of art, but were increasingly impacted by Bowie's drug use. He says there are times he can't even remember. He moved to Berlin with Iggy Pop to detox, and I love the "Berlin Trilogy" (impacted heavily by Brian Eno) that came out of his heroin detox. But for the rest of Bowie's post-drug-use career, I think the only full albums that I care about are Scary Monsters and Let's Dance. He produced a lot of good SONGS over the next 30-40 years, but was never as consistently productive AND GOOD as he was during his first 10 years or so. And even Let's Dance had a LOT to do with the contributions of Nile Rodgers and Stevie Ray Vaughn.
I don't think people tend to discount the quality of rock and roll music that was produced under the influence of drugs/alcohol. So why do it with writers? HST's first 20 years of writing...were breathtaking. The rest was admittedly not as good. Hemingway fell off in his later years. Salinger disappeared and became a hermit.
Is the myth of HST buttressed by drugs and alcohol and guns and anger? Sure. But he had a tremendous body of work in his first 20 productive years, so I think his status is well-earned.