They do have a right to the profits. They inherited it.

If you inherit stolen property, you don't have a right to it—it can be taken away and you likely won't get a cent for it.

The King was basically just the largest land owner in the country.

This is not true. He didn't organically acquire more land than anyone else. He just killed everyone who said it wasn't his.

The Queen isn't just given those lands by the government. They are passed down. You don't have to think anything about the righteousness of monarchy, just the right to property.

Except that that property was, 100%, acquired using the assets of the state. The state defended it, paid to improve it and contrary to your statement here, the land was NOT passed by inheritence. It was passed to whoever was king. That includes multiple times where it was either taken by force or passed to someone by act of parliament. That indicates it is NOT, in fact, personal property, because it ignored the rules of inheritance whenever those would have given it to someone other than the king. To use a recent example, the lands by inheritance SHOULD have stayed in large part with Edward VIII after he resigned the throne, because he was still the oldest son. Instead, they went to George VI.

That indicates, with clear precedent, that this is NOT personal property, subject to the normal laws of inheritance. It is tied to the monarchy and the monarchy is an institution of state.

The rights to that land and everything else the royal family owns should belong to the state, NOT the individuals. They aquired it while acting on behalf of the state, used the resources of state to maintain it and passed it along with the title, not as a personal inheritance. If the monarchy was abolished, the right to property would hardly support the idea it personally belongs to the monarch when they were NOT personally paying for most of it—they were using the state to do so.