That song and dance to beguile the masses is how the ruling keep ruling. Does this really need to be spelled out?
Charles was executed because he, as king, was in conflict with his own set: the ruling class. It was a civil war. But if he was in accord with his class you can bet your pretty neck that it would be in jeopardy if you went againt that ruling class.
> Charles thought as King he could do whatever he wanted
That is right. A monarch is there so that an entire class can do whatever it wants. But s/he will not fare well if they act against the class that upholds their reign. It is the same exact precise equation the world over modulo some rare historic exceptions.
No, it's operated for and on behalf of the Government. Notionally "His" Government, but we elected it, so it's ultimately our fault.
It's exactly like you've described for the Netherlands. Our Monarchs have no actual power, beyond the power that comes with being famous wealthy old white people anyway. English Kings haven't had real power over the Westminster Parliament since it executed King Charles in 1649.
Charles thought as King he could do whatever he wanted, Parliament disagreed, Parliament won and since he didn't accept that outcome they executed him. That's pretty definitive. He was dead, they were not.