While interesting, I'm not sure the actual map as pictured is a "good design": 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…
But map should be accurate in the first place. It's not like you can just ignore things you don't want to see there just because they are naturally to big and take up too much space
I'm trying to think of this not from a prescriptive position, though, but thinking of "why do people like Mercator". And I believe that people like the perceived efficiency of Mercator, in the sense that you can make a world map that fills more of its area with land mass.
Or, addressing your comment more pointedly: yes, yes you can. You can ignore the Pacific Ocean on a world map most of the time. :D