If there had never been a monarchy, yes it would be bollocks, but as there is it is simple common sense. If the monarchy was disolved tommorow - all of that estate would remain with them - SO no, it isn't bollocks. My point is simple - depsite a lot of peoples views to the contrary, the monarchy don't really cost the tax payer a bean, because it would cost a hell of a lot more for the government (nee tax payer) to buy and administer or rent the properties from the Crown Estate, which given that in owns half of central London, would be necessary. If that estate was in other private hands, the governement would have to folk our hundreds of millions of pounds more every year, rather than paying the queen an annual duty. I can't put it simpler than that.
Why would it remain with them? The Crown estates are a function of being the monarch, there's nothing to say if we turned into a republic that the Windsors keep all that land (that would be pretty unique in the history of dissolved monarchies tbh). As for whether it would cost the government more to deal with the Crown Estates without a monarchy, I very much doubt you've got anything to back that assertion up. You don't know a. the value of the land, b. what the government would do with it c. the incremental cost to the state of paying rents to private landlords on former crown estates (minus the windfall of selling the land in the first place), so basically you're making shit up.
You are assuming that removing the monarchy is as straight forward as Alan Sugar pointing at them and saying "You're Fired!".