Most pottery throughout history of glazed pottery has not glazed the bottom of vases. There is the practical problem of keeping the hot liquid glaze from fusing to the kiln shelf. A glazed bottom also makes for less friction for the bottom of the vase and it can slip and slide on what it is sitting on.
It's just my opinion, but glazed bottoms look amateurish and cheap to me, either that or it looks like a mass produced piece.