The idea of Monarch being head of State has merit in theory, but in practice, because the Monarch can’t actually use any of their executive powers for fear of upsetting norms, all it does is put all of the executive powers in the hands of the Prime Minister and leaves parliament the only thing holding the PM accountable. Charles couldnt actually use his powers because to do so would make everyone reconsider why he has them.
A comparison with the US doesn’t make sense, as it’s a fully presidential system.
Ireland, Germany, India would be better examples of a semi-presidential state we’d become without a Monarchy, depending on how the new head of state was elected.
I would imagine most people have never heard of Droupadi Murmu, despite the fact she controls the second biggest military in the world.