Why does replication require primers while transcription does not?
I'm no expert at transcription but from what I can figure out here and here transcription requires a promoter region acting as a template-directed mechanism for allowing transcription, which presumably bear a certain sequence recognised by the RNA polymerase and associated complexes. However DNA polymerase requires primers to guide it to the correct location on DNA.

EDIT: In light of comments below, according to here and here, RNA polymerase is capable of de novo synthesis meaning it is capable of initiating synthesis of RNA without primers and this is done by RNA polymerase binding to two nucleotides rather than nascent RNA polymer and a single nucleotide. Initiating nucleotide hold RNA polymerase rigidly in place, facilitating chemical attack on the incoming nucleotide. For bacteriophage T7 RNA polymerase, transcription begins with a marked preference for GTP at the + 1 and + 2 positions. DNA polymerase cannot add primers, and therefore, needs primase to add the primer de novo.