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A large creature occupying four hexes (in a cross shape) will take up three lines, which means the battlefield will have to be even larger, but then all of this won't fit on a mobile screen.
Drunken movement vertically, yes, but many people like hexes because movement in all six directions is symmetrical, whereas in the case of squares, the diagonals turn out to be longer.
Personally, I think this isn't particularly important, but the size of the battlefield is a rather significant drawback.