I think royals have health problems. And as they age, they will come down with more. We all have to die of something. As you age your diseases become more numerous from wear and tear on the body, and just your organs etc getting old. Many royals smoke. So I agree that they will have problems with that. I do think they have the oportunity to be healthier as they have more money to have a nice gym or trainer. They also can have a cook, and some control over their schedules for relaxation and hobbies.
I know Victoria of Sweden also suffered from an eating disorder when she lived in US. I can't remember which one it was. Masako has had her adjustment disorder for many years now. Recently she has started to make one or two public appearances. They really won't say what is wrong with her. Her mother in law the Empress also sufferred from a mental condition.
Little Lady Louise was born with an eye problem which has been fixed. Diana had slimers disease, and some mental problems. King Hussein of Jordan had cancer I believe which he went to the Mayo Clinic for treatment.
I know Crown Princess Mary takes health and fitness very seriously. She convinced Crown Prince Frederick to give up smoking.
I don't know if other royals have fitness regimes.