I wonder how many of those wanting an American style government realise that Sovereign immunity exists in the US, where it applies to Federal and State governments. It was derived from our laws.
It means that the government cannot be sued without its consent, although it can wave that consent.
I can quite understand why our Sovereign, embodying the state would still be in this position. However, it could well be time to limit the members of the Royal family to whom it applies. As Prince Charles has already shown he wants only a small number of the family involved in State roles, it would not surprise me if he did not encourage this. (Just in case someone doesn't understand this paragraph is opinion, not fact).
Our Constitution changes and moves forward all the time. Again, in my opinion, that adds to our stability. However, we live in an unstable world at the moment and it's an instability that has been deliberately caused by some for their advancement and wealth. I can imagine a deliberate attempt to destabilise us further by inciting groups to turn against the Sovereign and, therefore, our government and democracy.