Yes, there seems no likelihood the ancient system will be changed anytime soon. On the assumption we accept what "is" at the present imho I feel more optimistic if anything as KC3 is far more in touch with people of diverse creeds, ethnicities and background than any of his predecessors.
While he is stepping back by necessity from previous activism I wouldn't be surprised if his weekly meetings with any PM will allow his views to be subtly assumed and therefore filtered down.
Actually Charlie is not well received by some, and in high places, some around him just think he’s not fit for purpose as King. He’s had a tough childhood and well into his adulthood. He will have to keep his trap shut on some of his hair brained ideas, also step away from his charities, some have been viewed as suspect at the least involving baggage full of cash. Obviously he has his followers, but unlike the Queen who was admired by everyone practically not only here but abroad as well.
Purely on a personal point of view Charlie always came across as very nervous and fidgety and did not fit well into his position. Given that he’s now King, watch the lackeys round him crawl up his rectum. Again just my thoughts.
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