I think a lot depends on how long he's in the big chair. The media plays a much bigger part in shaping public opinion than most people are willing to admit and his ongoing relationship with them will be critical.
When Ugly Prince Charlie first jumped the broom, the media fawning was nauseating, as was seeing how many sheep willfully went along with it. The national hysteria was much the same then as we're seeing right now. During the years either side of the marriage breakup, Chuckie was reviled and hated. Many were predicting the fall of the monarchy back then.
Right now, he's Superman again and why? Because it sells newspapers and generates clicks. Even sensible and cultured sophisticates like the members of P&B are reading stories about him. Only to ridicule, obviously, but that still generates ad revenue. Once the novelty of the Coronation has worn off and people get back to their desperate, miserable lives, it's quite possible the media will turn on him again. Given time, it might just be enough to bring the country to its senses.
But if he crosses the Styx to join Maw & Paw before too long, Good King Billy will take on the golden hat and so far at least, he's beloved by the great unwashed. We'll just have to wait and see how well the PR bods can keep him in public favour.
Sadly, I can see the monarchy still being in place by the time wee Geordie steps up to the penalty spot.