Eucalyptus trees shed their bark to make it difficult for insect pests to maintain a home,
or simply to avoid the expense of upkeep (bark requires constant replenishment of oils to maintain its elasticity)
and as an adaptation to a to being a fire-loving tree in a fire-prone environment.

Eucalyptus usually requires fire for germination and by having lots of dry bark
(and flammable leaves) around the base of the tree is a great way to encourage fire.