How would this help?

It helps because as far as the supplier is concerned, your switchfuse is the
consumer unit, so they no longer care where your actual consumer unit is.

The customer's fuse would need to be able to discriminate with the
"electricity board"
fuse to be of much use.

There is no need for discrimination. Quite frankly who cares if it is the
switchfuse or the supplier's fuse that blows.

Christian.