  We consider the fundamental group $\pi$ of a surface of finite type equipped
with the infinite generating set consisting of all simple closed curves. We
show that every nilpotent quotient of $\pi$ has finite diameter with respect to
the word metric given by this set. This is in contrast with a result of Danny
Calegari that shows that $\pi$ has infinite diameter with respect to this set.
Furthermore, we give a general criterion for a finitely generated group
equipped with a generating set to have this property.
