Why don't the royals pay death duties.?

Only the monarch is exempt from death duties, the rest of them put their money in banks that are only accessible, by travelling through twenty or so different countries and doubling back in the last ten.

They don't pay for anything

All royals except the Monarch do pay tax.

The Monarch/Crown needs to maintain wealth to keep significant historical buildings for the use of the BRF and to provide an independent income so as to be free of relying on any government of the day and so to remain apolitical. The continuation of the Constitutional Monarchy is still what most of the UK prefers.

Everyone pays them except the monarch.

https://www.gov.uk/inheritance-tax

No 'death duties'. Inheritance tax.

There are no death duties. There is inheritance tax and that is paid by all royals except in the case of Sovereign to Sovereign transfers. Inheritance between spouses is exempt it is for anyone else. This has been allowed as many of the assets such as palaces, Crown Jewels and the Royal Collection held by the Sovereign have nil value since they are held in trust and cannot be sold and are already of benefit to the nation.

It is only the monarchy who doesn't have to do so---the rest of the family does; they have to pay inheritance taxes. Princess Margaret's children sold some of her things at auction in order to meet these taxes.