Problem with that is, as John Adams said, the US Constitution “is made only for a moral and religious people; it is wholly inadequate to the government of any other”, whereas Hawking sees the human race only in Darwinian terms of viciousness overruling any other quality and so would not even understand something like the US Constitution and how it would function if applied.
He may have been correct in the sense that a moral people would be the only kind to be able to maintain it long term; one look at the grotesque body of law that currently burdens the country in contravention to the Constitution's clear language would (and does) make strong men pale, and would prove his point. Nevertheless, so far as we maintain a vestige of morality and yes, religion, we may manage to hang on by our fingernails. It looks like a pretty close-run thing at the moment, I'll grant you.
I see the issue with him differently.
He believes, as most liberals do, that man is not inherently flawed, that he is perfect, and that his environment makes him evil. Liberals like Stephen Hawking feel we should develop a government that is constrained by specific rules which is far more granular and detailed (what government should DO) as opposed to guided by specific ideas which are less granular and less detailed (what government cannot do).
They think that if we do that, men won’t simply steer around the specific rules that state what should be done and engage in activity that shouldn’t be engaged in.
Conservatives (and the founders) believe that man is inherently flawed, and government should be constructed in such a way to inhibit men from realizing and expressing those inherent flaws in the service of government, lest they become tryannical.