TV producers think that most of the public would like to see some royals come out sing, dance or tell jokes (and make a general fool out of themselves.)
(In addition to the current royals doing it for free).
But - in developing the show - they define 'royals' broadly as one of the 600 aristocratic families of Britain - so as to have enough contestants for their show.
(Most 'aristos' have some drops of royal blood anyway.)
And thousands of them have legitimate 'coats of arms' due to ancestry.
Most younger royals have historically been horny fellows and even the kings have had multiple mistresses.
So, there is a lot of royal blood floating around in various personages.
There is also the chance that of one of the younger, real royals would being tempted to exhibit their musical talents - if it can be done anonymously.
Since many of the royals were in amateur theatricals when in school.
It is not impossible that 'bad boy' Andrew - bored with his current existence - would don a top hat and mask and dance along with some nubile young chorus girls.
Most royals have a very boring (but well - paid) life - sad but true.
(Basil Blathering - bringing you gossip of all things royal.)