One of the strengths and success criteria of the Mercator projection is that it allows us to largely ignore the vastness of the Pacific Ocean on our maps. Notice how much of this map is taken up by it. While interesting from a planetary perspective, it simply isn't that important to everyday life of most map users.
The proposed design thus has too low a land area to map area ratio to be very useful.
The projection itself would be useful as a digital map (with zooming and panning) or as an icon, though.