I've never seen an electric starter on a commercial jet engine( except APU) before although I think the 787 will be the first with it.
My guess will be the weight savings. Modern jet engines with their huge size will need electric starters of a few hundred kilos compared to air starters which only weigh abt 20 kgs max. And i believe that the 787 has an electric starter that can also function as an IDG. Could be wrong there, but remembered reading somewhere abt that.