To be fair, Charles and his sons do have a lot of duties they deal with. So it's not all jetplanes and parties.
Throw in the Queen as a general UK Ambassador type and the figurehead of state and spirit of the nation, and they do put in the effort.
Say what you want about the majority of countries around the world, but state visits by the Queen and the immediate family can do a lot of good diplomacy for the country.
Just because it isn't all in strict "official" form of diplomacy ...
Well, it might make you feel good about yourselves and it might be entertaining, but it's undemocratic. Why not get some more healthy traditions which don't include showering one family in wealth and castles in return for the strenuous duty of handing out the honours list, doing a few charities and receiving dignitaries.
The French had it right, off with the head and no feeling sorry after the fact.