It seems to me that a directed acyclic graph, rather than a tree, is a more accurate model in this case. (Directed because time always flows in one direction.)
A phylogenetic tree also fails to capture information about life that people might reasonable find interesting. Suppose for instance you want to study all organisms that fly. Bats, birds, insects and pterosaurs all fly[flew] but don't share common flying ancestors. The "flying organism" classification doesn't fit into that simple hierarchical tree.