I think part of the fact is that Gaap is pretty much the only summoned thing (as in Virgilia or Ronove) that doesn't have a known vessel. And seeing how the vessels usually correspond to people like Kumasawa (honestly not entirely sure what she is) and Genji (furniture)... That leaves Shannon, Kanon (seen an image of him in Gaap's dress), Gohda (same here)... And Nanjo.
That or Gaap's outfit might as well be a meme, seeing how several characters are drawn with it
So, duh, choose the fat old man to wear it. Thrown in George for a bonus