What is the beneficial function of IgE antibody?
No, they are of course not there to cause allergies.
It is thought (although not directly proven in human) that IgE is important to fight parasites and worms. They bind to antigens from the parasites, which leads to the secretion of histamines. This causes a local immune reaction (which also is a problem in allergies) which is helpful to fight the parasites.



See these papers for example:


IgE, allergies and helminth parasites: a new perspective on an old
conundrum.
IgE Enhances Parasite Clearance and Regulates Mast Cell Responses in
Mice Infected with Trichinella spiralis
Immunology of Parasitic Helminth Infections


There is also some evidence, that IgE is involved in the immunological response to cancers:


Activity of human monocytes in IgE antibody-dependent surveillance
and killing of ovarian tumor cells.
Animal models for IgE-meditated cancer immunotherapy