I think there is something in this "curse of the comedian". But I don't think it's a given.
Many comedians are addicts of one kind or another
There seems to be a stronger link between addiction and comedy, though. I do think the kind of person who is drawn to performing for laughs is more likely to become a drug abuser and/or alcoholic than most people. There are numerous tragic examples of this tendency from the top echelons of comedy performance, with Williams himself being the latest one.
I've also got my own experience to draw from. I've been a comic, and while I haven't ever abused drugs or alcohol, I do have other addictive tendencies. Currently I'm addicted to blogging and social media, for example. And I've long been a bit of a workaholic.
Then there are the things I've seen while involved in various comedy scenes across Australia. When I was performing standup in Melbourne back in the nineties, for example, I was always amazed at how many of my peers smoked dope regularly. Some of them were into harder drugs, too.
I think that this had something to do with comedy being such an intense, nerve-racking occupation. Being a highly strung type myself, I would usually have a glass of wine before performing. Many others would fortify themselves in a similar way, or with a joint!
After the gig you'd be buzzing if it went well, down in the dumps if it didn't. Many felt chemical assistance was required to regain composure after either of those outcomes!
Comedy performance does make you "high"
As well as the chemical assistance comics often use before and after doing the routine, they get a powerful adrenalin and endorphin rush during the performance itself. Making a crowd of complete strangers laugh repeatedly for an extended period of time is a big challenge with huge potential pitfalls, after all. You risk public humiliation if you fail. And that's something most people fear deeply. So you're certainly amping up your nervous system merely by attempting it.
This proves that comics tend towards being thrill seekers. And there certainly is a thrill involved. The sound of laughter in all the right places is like music to your ears. Better, actually. As well as the fact that it's a kind of affection that you're getting, it also gives you a huge sense of power. Intoxicating is not too strong a word.
If you experience that even once odds are that you're going to seek it over and over again. And if you start getting paid for it, well, that just makes it even more rewarding! For many comics doing a gig every week or two is enough to satisfy that craving. But some others have a much greater need for this buzz, and seek it much more often than most. As well as constantly doing gigs, they're always "on". Robin Williams was a classic example of this syndrome. He was forever chasing the high of making people laugh.
Robin Williams was hooked on laughter
And when he couldn't get it, he still had to get his kicks in some other way. It was as if he just couldn't bear the grinding reality of, well, reality. So early on in his very successful career he found relief in drugs and alcohol. It didn't take him long to realize how destructive these things could be, of course. And he managed to swear off them for many years.
Obviously being a laugh addict was not so toxic in itself. But constantly seeking out that still potent high must have taken a toll, too. I'm not saying that comedy killed him. But I do think Williams, like so many other comics, was a slave to the thrill of making people laugh. And that deep psychological need did have something to do with his chronic depression and ultimate suicide.