One big difference between the UK's historic constitutionalia and the US is that the UK generally recognises that we only do things a certain way because agreeing how to change them is too hard, while the US appears to think that they do things in their certain way because that's the right way to do them.

Specific examples for the UK: inducting politicians into the Privy Council in order to qualify them for security briefings, Henry VII powers, and ministers' authority deriving from the seal they're given by the sovereign. Which would almost make as much sense if it were a marine mammal as it does being a stamp.

The thing being, they work well enough. And if you want to replace them, you need to work out what to replace them with and how.