Pictures here - again, text in Swedish.
An explanation (not a translation): My friend Åsa enjoys medieval re-enactment. She kept seeing cusion covers with diagonal patterns in old pictures. At first, she just thought: "nice diagonal patterns". Later, she decided that fancy looms were (probably) not as common as the diagonal patterns were... and had an AHA-moment: weave simple plaids, cut the covers on the diagonal, make an envelope-style cover.
She says that the cushion also looks nicer and softer without the seams at the sides.
I want to add something about the tassels. It was once common to have extra cushions stacked in a corner, to be grabbed as needed. Such cushions often had tassels to be used as "handles". Thus, the tassels had to be firmly anchored - this is how: make a tassel with a firm "head". Place the head inside the cover, stitch through both cover and tassel "neck". Such "handle tassels" could be made of almost anything - often from rags - as they were more an utility that an embellishment.
A picture of such a cushion can be seen here (scroll down a little). (But the fabric is used the "ordinary" way - straight)