I would personally prefer to have that decision be taken by a governmental agency or anything else managed by an elected person. Now, I'm not a US citizen, and I have zero trust in the current US administration, but in a "normal" context I would want to have at least some governmental overview of the shutdown process instead of delegating the full power to a private corporation.
Edit: In a "Trump" context, I really don't know... Really sad to see this country dying slowly.