Will the Monarchy Survive?

I hear people saying Prince William and his lovely wife Catherine, along with their beautiful children are the modern face of the British Royal Family. I agree, yes, right now they are.

But hang on, the Queen has died aged 96. She was a link back as far as the 1920's, basically the whole twenty-first century. Impressive. But now we are entering a new phase, returning to normal as it were, with males ascending the throne, all of them old and ruling for 20-30 years before the next takes over. Let me explain:

King Charles is 73, coming up to his 74th birthday in November. Given the age at which his parents died, he has about 20 years at the top to look forward to. After him will come his son William, currently aged 40. When he takes over from his father he'll be 60. If he reigns for 30 years, his son will then come to the throne aged 59. 

Rounding this, failing abdications or unexpected deaths, the next 80-90 years will see a pale, stale, older male on the throne. The twenty-second century will arrive and no female in sight. Male primogeniture may have gone, but it makes no difference in this scenario.

I'm not convinced the British Monarchy can survive, given the direction society has taken and contrasting with the feudal system currently in place.