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I would put the manufacturers choice of using either linen or leather as the sharpening side of the strop down to:
Cost
Availability of material
Prestige
design choice
Gimmick
and others if I...

Canvas/Linen strops were and are for sharpening the edge and as Seraphim points out, the canvas/linen also makes a great foundation for pastes. I very much doubt that the Linen was EVER referred to...