Go and have a read up about James II. Legally his status was deemed to be an abdicated King, even if he didn't like that. And it remains so for his descendants.
Also I suggest you have a good read around exactly what William and Kate get too. For a start, they would have to pay for their own security. Private security. They would have to meet the costs of recruiting, training and all the other associated employment costs. Their security would no longer be sourced direct from the police and the army so they wouldn't be able to tap into their systems.
They would no longer have access to the Royal train or the Royal flight. Their access to the rail system would become the same as anyone else's and they'd have to pay for jets and helicopters.
They would no longer have special status and diplomatic immunity travelling abroad and would no longer have access to government departments to ease their way around the world.
They would lose access to the Royal Palaces and their security systems. They would have to live in privately owned houses and pay for upkeep and renovation themselves.
With the loss of their status a lot of the rich friends who currently provide their private yachts and islands would melt away with their Royal cachet.
The royal family are rich, but they are not that rich. The idea that they could carry on leading the lifestyle they do with just their own funding and a dibs on the Duchy of Cornwall is laughable.
They are not oligarch rich. They are not palaces, yachts and private islands and jets rich. Look at what Diana's life was like when she lost access to all those things, she became dependant on rich friends to maintain the same lifestyle.