When I quit my job last year to join a start-up the cost to continue my COBRA benefits would have been $700/month (and I'm a healthy guy in my 20s). Fortunately, I'm in MA with its private health insurance market, and I was able to find a plan for $200/month. I still had to go without health insurance at all for a month, though, to make myself become inelegible for COBRA and therefore eligible for the other plan.
"Not the cheapest thing in the world" is quite an understatement.
From what I'd found (also for a young single person), it would have been more like $500/month, but even at $700, that's still cheaper than rent at any apartment I've seen since I was a college student.
And remember the context: this is someone who wants to take a year off with no work at all, and so is voluntarily giving up tens of thousands of dollars, in exchange for his own time. Yes, there are almost certainly cheaper health insurance options, depending on how much effort you want to put into the research, but COBRA is the upper bound, and takes practically no time to sign up for, which, again, was the whole point of the exercise.
"Not the cheapest thing in the world" is quite an understatement.