RNA polymerase does not require primer because
RNA polymerase active site geometry allows de novo initiation without oligonucleotide primer. Structural studies reveal holoenzyme accommodates initiating NTPs at positions +1 and +2 base-paired to template DNA within catalytic cleft, stabilized by Watson-Crick interactions and base stacking with sigma factor contacts. Formation of first phosphodiester bond does not require pre-existing 3' hydroxyl unlike DNA polymerases. Consequently polymerase can start RNA chains at any promoter-defined site. This fundamental difference between replicative and transcriptional enzymes enables transcription to initiate spontaneously at regulatory signals without primase activity, simplifying gene expression control.
Ref: Watson et al. Chapter 13: RNA polymerase de novo initiation mechanism no primer required; Alberts Chapter 6 Active site NTP stabilization