I think as devs we often think of our site or application as the center of the user's universe, but I don't think users memorize the minutia of our applications like we think / would hope.
Also, I actually worked with folks in abusive relationships at one time, their actions are not as predictable as you might hope.
I'm guessing gov.uk is hoping that this will become some kind of standard, at least for British resources.
I thought this was a tool that users specifically install in order to browse any content.
But instead it seems this is simply a feature so that users that browse gov.uk websites specifically can exit.
Jakob's law is a thing but I actually think in the case of GDS they are in the fairly rare position of perhaps being able to justify the hubris you speak of slightly.
Not only are they directly or indirectly responsible for the UI of a frankly staggering number of online services, they are also one of the most influential bodies - perhaps in the world - when it comes to this sort of thing.
For the user I think that still means asking them to memorize something odd for a very limited use case that you won't think of visiting any other government site.