Hopefully he had significant assets that didn't go through probate. There are dozens of ways to get around it. Insurance policies, most retirement accounts such as 401(k) pay directly to a beneficiary, and joint ownership of many things such as real estate can be a way to bypass probate. Depending on what countries he had assets in, trusts may have been an option. Anything he transferred into his kid's name wouldn't have been part of the estate. He didn't have a profession that lent itself to a pension, but where pensions still exist there is sometimes an option to select a 50% lifetime payout to a specific relative who doesn't necessarily have to be a spouse. I know people who, having divorced or having never married, put their pension in the name of a child or grandchild. Even just a $2k per month payout, over a person's lifetime, is instant FIRE for most of us. For a youngish person who is just starting out, it pushes him or her to the level where they *can* take a chance on a career in the arts, or as an entrepreneur. I doubt even 10% of my assets will end up in probate.
It may be worthwhile to have a discussion about the extent to which financial trouble can affect a person's will to live. I'm not saying that it was the case for Anthony Bourdain, because I don't see sufficient evidence to support that conclusion.