It could happen in theory, but it won't. The Queen has always seen being monarch in terms of duty, as did her parents. Monarchs of countries such as the Netherlands may see it as a job from which they retire when they get old, but not her. The shadow of the abdication of Edward VIII, which shot the Queen's father into the stress of a public role he never wanted (which the Queen Mother always believed was a major factor in his early death) has always loomed large. With all the hoo-ha over Harry stepping back from being a senior royal, comparisons were repeatedly made: an American divorcee (not that being a divorcee matters so much in the 21st century - look at Charles and Camilla - but still), causing a royal to choose her over his "duty", which in turn led to a life abroad. Note the wording of the Queen's announcement that Harry and Meghan were permanently removed as a working royals, losing their titles and patronages: they would not "continue with the responsibilities and duties that come with a life of public service". That's how she sees it. Not to continue until her death would be unthinkable for her. As for Charles, he's waited a long, long time to be King and clearly wants it - he said in the run-up to his marriage to Camilla that he was going to have her and be King. So I can't see him passing it up when the time comes. So William will just have to wait his turn.
Good point, Lianachan, about Charles not necessarily taking the name Charles III - although Charles II ultimately fared rather better than his father did. I guess we'll see. "King Arthur" has too much resonance, but George VII or even Philip is not unthinkable.