There are many countries in the world who run different system of governments, and many as doing it quite successfully.

That phrase implies that she had PMs subservient to her. That's not how the UK monarchy is generally explained, at least not outside of the UK.

Under Charles III’s reign, it will be His Majesty’s government; how actively he takes an interest in its affairs will be on him, but at a minimum laws will not take effect without his assent and his permission will be asked for to form future governments.

That’s the system of the United Kingdom. It never stopped being a Kingdom, people just chose to view the late Queen as ceremonial because it was a convenient way to square the Throne with democratic ideals, but it really isn’t all that ceremonial. The reason the customs held fast is because Queen Elizabeth II worked to make the system work. A different sort of Queen may have sparked a constitutional crisis or two by now and there’s no guarantee she would have necessarily lost to the Commons.

Wait, you mean to tell me the King can veto laws in the UK? I thought you guys figured this loophole out? Who controls the military?

The functions and powers of our Presidency are a much closer derivative of the British monarchy than we tell ourselves in our classrooms. The President signing bills into law is a copy of the requisite assent of the monarchy. Political appointments were a copy of how the King vested power, and as you guessed it, the King is the Head of the British Armed Forces.

Also I think even British folks are undersold on how powerful the late Queen really was. She may not have vetoed any legislation, but her Prime Ministers sought and received her advice regularly, consulting with her and unburdening themselves to her the problems they were faced with or tasked with resolving. Put another way, she was an active participant in how laws were formed and the business of Her Majesty’s governments proceeded even if she did not participate in the drafting of the texts or have any policy objectives per se. That isn’t ceremonial at all, although many of her duties as Queen and Defender of the Faith were ceremonial.

In America we celebrate the separation of powers, telling ourselves a few myths along the way about the co-equality of branches (essentially Nixon era propaganda from when he was facing down the gun barrel of impeachment, but Congress adopted the myth despite being head and shoulders the most powerful branch of Government under the Constitution). The King-in-Parliament—or under the late Queen, the Queen-in-Parliament—is absolute power in the United Kingdom and no one may question their directives because this is King, Lords and Commons speaking as one. Their power as one body is what we separated into the President, Senate, Representatives and Supreme Court. We then limited it further by conceiving of powers as enumerated, although clearly this was insufficient as a power limiter.

In reality, if King Charles started vetoing then after a short constitutional crisis, parliament would basically just change the rules of the game to say that the monarch no longer has the power to veto laws.

If the monarch tried to actually do something significant with that power I imagine the law would be changed pretty quickly.

This is why working royals generally have various military titles and positions, because the monarch is the head of the armed forces. It's also why the monarch dresses in military regalia for various military events.

The royal family is little more then a Kabuki act at this point, no reason to throw out tradition on a whim.