Personally I really like viewing the Koudai or feet of a piece, as I feel it really helps me get to know the piece so much better. In fact I have many pieces some basically completely coated in glaze and others with a nicely and fully exposed foot. I personally like being able to feel the fired clay and view the composition of the clay. This also goes for the artist mark, and I am not fond of pieces in which the artist mark or chop has been completely covered by glaze.
For example this piece rather rubs me the wrong way, the foot is nearly completely covered in glaze and most confusing is while there is some exposed clay at the very bottom of the foot, the carved area in the center which normally bears the stamp of the artist is completely glazed, and in a black glaze so I can not even make out any sign of an artist stamp.