There's no agreed replacement system and the crown estate, where they get their money from, is owned by the government and makes more money for the country as a old king handed if over. Splitting those up would be a pain for sure even if I am a complete republican and think it's embarrassing.
Part of their money is also a lack of taxes. If they receive $10million from some source whether it is laundered money, from taxpayers, selling off a castle, or whatever. They are keeping nearly all of it. Same with the Biden family, Clintons, Trumps, and so on. Avoiding taxes at their income level is basically like having an additional two or three massive sources of income. When Biden is taking his 10% cut for the 'big man' or Hunter Biden is raking in $50million in consulting fees that money is going into some LLC or trust that is immune to the IRS probing it. Though with the level of corruption nowadays they probably just deposit the money into their own accounts under their own names at this point.
And even their laundering operations are immune from scrutiny. Where did Epstein get all of his money? Everyone knows it was dirty Mossad financing. But the governments still act like he was some big legitimate businessman. When Obama laundered money through his scam book deals or corporate speaking appearances he didn't need to worry about some IRS or FBI probe like a random criminal would.
Anyone want to guess how much money Bill and Hilary have reportedly made from speaking fees? Over $150million. That doesn't count book deals and corporate speaking events that are not recorded publicly.