Primers are used for DNA replication. RNA polymerase isn't used for DNA synthesis. If I remember correctly, RNA Pol doesn't have exonuclease activity meaning it doesn't correct nucleotide mistakes whereas DNA Pol has this function. This implies DNA fidelity > RNA fidelity.
Most likely DNA Pol, based on its protein folding properties, needs to recognize a short stretch of ds template so it "knows" where to start DNA replication.
stealth edit