Hi Luke, glad you are trying out straight shaving!
In order for this to make sense, you have to buy in to the belief that a linen strop is mildly abrasive, and a leather strop is minimally to non abrasive. So stropping on linen will abrade the bevel enough to partially offset the dulling effect of the previous shave, while the leather will help to straighten out the deflected edge resulted from banging into the tough beard stubble.
Stropping only on leather, while realigning the edge to keeness, will not remove an appreciable amount of metal, so eventually the edge is too dull to shave.
Stropping on linen removes just enough to postpone the need to touch up the edge on more abrasive mediums.
Everyone strops on leather prior to a shave, so it wouldn't be much of an experiment to "strop ONLY on leather".
If you don't believe in the use of fabric strops, I just wasted 5 minutes typing this out on the joke of a keyboard on my iPhone....

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