Correct, but that wasn't given to them by the US constitution. Rather, that power rests with each individual state constitution. Further, depending on the state, it can be anywhere from unlimited to completely bound. [1]

The role of "governor" isn't defined by any federal laws or rules. It's theoretically possible for a state to decide that it doesn't need a governor.

[1] https://ccresourcecenter.org/state-restoration-profiles/50-s...

> It's theoretically possible for a state to decide that it doesn't need a governor.

The guarantee clause (Article IV section 4) says "The United States shall guarantee to every State in this Union a Republican Form of Government..." What constitutes a "Republican Form of Government"? Is having a governor essential to it?

I think the answer is nobody can really say because the Supreme Court has never had to consider that exact question, and nobody knows how they'd rule if they did. They have previously ruled that the guarantee clause is "non-justiciable" (in Luther v. Borden, 1849), which implies they'd let a state adopt whatever form of government it likes, but they could change their mind about that if they wanted to.

What if a state wanted to adopt the Westminister system, like a Canadian province or Australian state? What would SCOTUS have to say about that?