The media has certainly plugged the line that the monarchy has never been stronger or more popular. I think there is a great deal of affection for and profound feelings of warmth towards the Queen, but I am less sure that this carries onward to the monarchy as an institution. While the Prince of Wales pretty much got things right and in tune with the public mood during the celebrations, this is a rare achievement and he generally lacks the charm of his mother. He tends to come across as arrogant, bad tempered, impatient, self-important, with a highly developed sense of entitlement and completely out of touch with the lives of the rest of us. It doesn't help that he has had to hang around for years waiting for his mother to die before he can do the job (such as it is) that he was born for. In spite of the work of the Prince's Trust, he remains, I suspect, an unpopular figure.
There are those who will never be willing to accept the Duchess of Cornwall as Queen Consort. Although she is de facto the Princess of Wales, royal advisors clearly recognised that calling her by that title would be deeply unpopular and so used the Duchess one. I'm not sure what they could come up with as a suitable alternative to HM the Queen.