4 mil. Poly tubing is my go-to... it protects the rugs for PU/delivery, is re-usable, and when it’s beaten up, I use it for garbage, or to transport dirty towels from the shop to be cleaned, or, cleAn towels back ...
Paper only protects for dry. Not all the oil and pre-spray's on your vans floor.
A shelf system in your van will keep rugs clean without wasting wrapping.
Paper is slippery and those pictures looked like a shoemaker was moving rugs around.