And I agree with you that it is not necessarily a positive outcome that a king's heir would assume the wealth of the king. However, I think the trade-off of using law to essentially plunder property (again, assuming the property was acquired through no act of injustice), undermines the purpose of law - to defend against injustice.
Property (acquired or created justly) is typically an outcome of liberty, and often fate (birth, luck, etc). I don't believe we can alter either of these conditions through tax law (force) without undermining the justice of law itself.
Furthermore, in my view, I don't believe an individual's property is something that anyone else has a claim to dispense with, especially a political organ such as the 'the state' (an entity which bears very little responsibility for the outcome of it's economic and financial actions).
That doesn't mean I necessarily like the idea of people amassing or acquiring resources without work. But the reason I work hard is to benefit the things which I choose to value: my family, my community, the erasing of Star Wars Ep. 1-3 from history, etc. I want to give my kids a better shot at life than myself. Property may be a component, but is far down the list from things like values, and work ethic. But these are my choices for my life. That to me, is the American Dream - to be free live how I choose - not wealth and things. Whether I am very rich at some point, or not - I don't believe force should be employed to negate or alter my choices, nor do I wish to use force to alter your's or someone else's.
Maybe I'm way out of my gourd, but the fact that Paris Hilton has a huge amount of wealth, and no values is a total failure of her parents - not the inheritance itself.