I have laid a high shine porcelain floor in a shop. Is it wise to use a doormat? 
Yes. This finish is not recommended for areas of medium to high traffic, but through the use of a mat or runner you can protect the polished finish and thereby maintain its durability and the desired effect.
It is very common to see mats used in entrances from external to internal areas covered with polished tiles. In the street, small stones and dust can become attached to the soles of footwear and so the door mat acts as a way to eliminate these particles from coming into contact with the tiles.