I agree.
But really, I think you also want a body which safeguards democracy, the use of the military and the rule of law in an apolitical fashion.
The Supreme Court can do some of the job, but they are a responsive body. Really, you need some folks who keep an active eye on it at all times.
I know Americans hate to hear it, but this is the useful role a constitutional monarch plays. The queen doesn't have executive authority. But she does sit atop the UK's trust architecture.
You can structure something without creating a monarch. Maybe a small body of super-eminent people who are NOT elected and which doesn't include politicians but whose main job is to make sure neither the chief executive nor congress behave unconstitutionally. Such a body would have value around about now.