I was actually taught to hit a second time with a cover sheet after peeling the carrier, and Diane at CYW, also recommends it with the print and cut she does for me. That said, with my normal cad-cut, I often get lazy and skip it.
However, a second pressing with different cover sheets can also alter the surface of the vinyl a bit.
This morning, I pressed some Easy Weed, peeled, and re-pressed a few seconds with baking parchment to increase the texture from the fabric's mesh surface. (I think that the baking parchment is so much thinner than the carrier sheet, it helps this process).
Teflon sheets are often billed as "producing a more screen print-like finish", and Diane and I have also worked with actual texture-producing sheets similar to ones used by upholstery repair folks trying to match original grain.