Maybe? That's a really complicated question honestly - how much of their personal property actually is hereditary wealth and how much is a benefit of their station. I can tell you the answer is neither 0% nor 100% - the royal family (if dethroned) shouldn't be thrown out as paupers and it shouldn't be granted personal control of spaces that enjoy public use. Where precisely that line should be drawn is complicated but if that line leaves them with any significant portion of their current titular wealth the UK will end up losing money. The Crown Estate might be worth around 15.6 Billion, so a few hundred million every year is far less then the family would receive if they liquidated the lands at value and just invested it into an index fund. The actual income of the estate is significantly higher - with a lot of those assets under reporting their actual yield in terms of tourism and public benefits.

I think it's a really complicated question.

Lastly, while we're on this topic - why hasn't the US seized the wealth of the 100 most wealthy individuals unilaterally - that money would be of immense amount of benefit to the country so why do we let wealth accrue?