I think the symbolism of the state (in this case embodied by the monarch, but it doesn’t have to be a monarch) as a separate entity from the “government” is very appealing. In this way, you can have certain offices that work for the state and others that work for the government. The state/crown side would be apolitical whereas the government side would be politically appointed. But it would be helpful to have the two sides explicitly separated to have minimal interference.

I have no idea if this is how the British monarchy works in practice, rather just the view from my side of the pond. In the US, we have the concept of career vs political positions in government agencies, but in practice, there is a great risk of interference between the sides.