That is a complicated question that comes down to the mechanism used by RNA polymerase to initiate transcription. Fundamentally RNA polymerases do not need primers because they have evolved to be able to initiate transcription at specific sites (promoters) that are thermodynamically favorable for initiation.

I agree with Michael J. Benedik. In cells, the process of transcription is primer-independent due to the properties of the enzymes and the intracellular conditions. However, in vitro (in a tube) transcription does require primers as you are utilizing a cell-free system.