It is highly recommended that a mulched or similar type cover be used at the base of all trees with a natural defined boarder edging.
The basic reason for this is so that the tree maintains its rightful moisture and nutrition level. When grass roots,and other plants, are in close proximity to the base of a tree, the grass roots take away moisture and nutrients from the tree. The base of the tree is similar to a mouth, and its essentials are delivered to the rest of the tree through the base.
Secondly, if grass is near the base of trees, when grass trimming is done, the grass trimmer may strike the base of the tree, causing irreversible damage and weakening. Protection for trees, arguably the most valuable part of a landscape, is imperative.