Presumably she doesn't because she rather likes the money and the palaces more than she wants to settle the question as to how you have a parliamentary democracy and monarchy with "you don't".
Besides, the scenario you depict further reinforces my argument that there’s a “trusted root” at the apex of our democracies and that this entity (whether the Queen, or Parliament, or Congress, or the President, or whatever-have-you) can pursue its own interests with abandon, and there’s nothing we buggers further down the pyramid can do to prevent it.
It's far less terrifying to me that the present Queen can do that than that any oligarch with a £100M to spare can probably "lobby" to get the changes they want.
The royal family are in a dicey position, but I trust the current Queen more than MP s in general, but perhaps less than the 2 Houses as a whole. She can probably do anything that goes with either Parliament OR with the demos but couldn't go against both.
Parliamentary immunity also exists in many countries to ensure that parliamentarians cannot be prosecuted for acts they undertook whilst in office (or other acts, so they that they cannot be compelled into anything).
You’re never going to get a body politic to pass a law that places them all at risk, and if somehow one got through, they’d pretty quickly pass another one to repeal it.