Their only privilege is that royal wills are private, unlike the rest of us
Not just that. They've opted out of certain regulations and taxes.
There's a history of royal exemptions from taxes. They only started paying taxes on investment income in 1993! And only because of a light shone on it. Prior to that, with a huge share portfolio, this would've saved the Queen and RF millions.
Also the two Duchys act like a company but pay no corporation tax or CGT unlike the public who run companies. Why should the Duchys have such huge competitive advantages in the property market against others?
Then of course IHT... which is why the Queen Mother left her whole £75M estate to the Queen... that meant no IHT.
I know some of the reasons but still think it's a bit rich to be exempted from all these taxes. But hey... we're just the plebs and pay up.