My All-Ett arrived today, and they weren’t joking about the (lack of) thickness! With the same contents, the new one is about a third of the thickness (less than 0.4 inches, compared to 1.1).
Here’s my old wallet:

And here’s the All-Ett, with exactly the same contents (13 cards, a couple of books of stamps, and some cash):

The picture below shows the empty old wallet next to the full All-Ett.

It only cost just over a tenner too, including postage from the US.