I think it's in relation to being a solid head of state (certainly applied to Liz), one who doesn't waver in times of trouble. They are always there, consistent, in the background, and can offer comfort.
There is no way in a million years you would start a RF now, people would laugh at the concept, but as this one has been there for a thousand years, so they carry all that tradition (and people generally adore tradition), it seems to work.
A powerless head of state, a figurehead, one who has had consistently high favourability among the public (certainly Liz, and Charles doesn't have that many detractors himself), one who is a key player in the soft power status of the UK and more than pays their own way, by pure chance this system works. Look at other heads of state around the world, generally despised.